Methods, systems, apparatuses and devices for facilitating motion analysis in a field of interest

ABSTRACT

According to some embodiments, a system for performing motion analysis in a field of interest is disclosed. Further, the system may include a plurality of motion sensors configured to generate a plurality of motion data corresponding to at least one motion of at least one object in the field of interest. Further, the system may include a communication device configured for receiving configuration data associated with the field of interest from at least one data source. Further, the system may include a processing device configured for generating a digital model corresponding to the field of interest based on the configuration data using a simulation module and generating one or more of a plurality of motion signatures corresponding to a plurality of predetermined motions and a plurality of object signatures corresponding to a plurality of predetermined objects based on the digital model using the simulation module.

The current application claims a priority to the U.S. Provisional Patentapplication Ser. No. 62/617,502 filed on Jan. 15, 2018.

The current application is a continuation-in-part (CIP) application of aU.S. non-provisional application Ser. No. 16/197,725 filed on Nov. 21,2018. The U.S. non-provisional application Ser. No. 16/197,725 claims apriority to a U.S. provisional application Ser. No. 62/589,287 filed onNov. 21, 2017.

The current application is a continuation-in-part (CIP) application of aU.S. non-provisional application Ser. No. 16/231,004 filed on Dec. 21,2018. The U.S. non-provisional application Ser. No. 16/231,004 claims apriority to a U.S. provisional application Ser. No. 62/609,594 filed onDec. 22, 2017. The U.S. non-provisional application Ser. No. 16/231,004also claims a priority to a U.S. provisional application Ser. No.62/617,502 filed on Jan. 15, 2018.

TECHNICAL FIELD

Generally, the present disclosure relates to the field of dataprocessing. More specifically, the present disclosure relates tomethods, systems, apparatuses and devices for facilitating motionanalysis in a field of interest.

BACKGROUND

Motion is one of the most crucial piece of information. Early beforeachieving any high resolution, nature developed vision for motiondetection and control for the critical purpose of survival, defense andhunting.

Motion analysis may be used for motion detection and/or moving targetrecognition applications. These applications may include motion analysisin sports fields, militarized sites, or even in research laboratoriesetc.

Further, the drawback of conventional motion analysis systems that maybe based on numerous video cameras are multi-fold and the followingitemizes the most important disadvantages:

1. At a sensor layer, the trends in constructing video cameras are tomove to higher and higher pixel density in order to improve the imageresolution. Increasing the resolution diminishes the sensitivity. Butsensitivity is the property needed to detect changes of contrast in theobserved scene and especially in dim light. The move to high sensitivityleads to using detectors that work each as an independent pixel thatcount photons. High sensitivity requires to develop large fields ofview, a move that diminishes the resolution.

2. At the telecommunication layer, each video camera produces acompressed bit rate of several megabits per second (Mb/s) that has to betransmitted in real time, or stored but not yet analyzed to detectmotion. For example, compressing HD video with an original samplingresolution of 1920×1080 pixels using an MPEG4 standard with a constantframe rate of 24, 25 or 30 progressive images per second (image/s)generates bitrates that range from 5,000 to 10,000 Kbit/s. The file-sizeof the compressed video may range from about 400 MB to 750 MB(Megabytes) after 10 minutes and 6 times those amounts after one hour.

3. At the application layer, all video information still need to beanalyzed in real time to unfold the embedded motion.

Therefore, the “camera-everywhere” involves a huge amount of data thatneeds:

-   -   To be transmitted that would overpower the telecommunication        network, and,    -   To be processed by the application layer that would be        untraceable or unmanageable in real time for an intelligent        system.

Therefore, there is a need for improved methods, systems, apparatusesand devices for facilitating motion analysis in a field of interest thatmay overcome one or more of the above-mentioned problems and/orlimitations.

BRIEF SUMMARY

This summary is provided to introduce a selection of concepts in asimplified form that are further described below in the DetailedDescription. This summary is not intended to identify key features oressential features of the claimed subject matter. Nor is this summaryintended to be used to limit the claimed subject matter's scope.

According to some embodiments, a system for performing motion analysisin a field of interest is disclosed. Further, the system may include aplurality of motion sensors configured to be disposed in the field ofinterest. Further, the plurality of motion sensors may be configured togenerate a plurality of motion data corresponding to at least one motionof at least one object in the field of interest. Further, the system mayinclude a communication device configured for receiving configurationdata associated with the field of interest from at least one datasource. Further, the system may include a processing device configuredfor generating a digital model corresponding to the field of interestbased on the configuration data using a simulation module. Further, theprocessing device may be configured for generating one or more of aplurality of motion signatures corresponding to a plurality ofpredetermined motions and a plurality of object signatures correspondingto a plurality of predetermined objects based on the digital model usingthe simulation module.

Both the foregoing summary and the following detailed descriptionprovide examples and are explanatory only. Accordingly, the foregoingsummary and the following detailed description should not be consideredto be restrictive. Further, features or variations may be provided inaddition to those set forth herein. For example, embodiments may bedirected to various feature combinations and sub-combinations describedin the detailed description.

BRIEF DESCRIPTION OF DRAWINGS

The accompanying drawings, which are incorporated in and constitute apart of this disclosure, illustrate various embodiments of the presentdisclosure. The drawings contain representations of various trademarksand copyrights owned by the Applicants. In addition, the drawings maycontain other marks owned by third parties and are being used forillustrative purposes only. All rights to various trademarks andcopyrights represented herein, except those belonging to theirrespective owners, are vested in and the property of the applicants. Theapplicants retain and reserve all rights in their trademarks andcopyrights included herein, and grant permission to reproduce thematerial only in connection with reproduction of the granted patent andfor no other purpose.

Furthermore, the drawings may contain text or captions that may explaincertain embodiments of the present disclosure. This text is included forillustrative, non-limiting, explanatory purposes of certain embodimentsdetailed in the present disclosure.

FIG. 1 is an illustration of an online platform consistent with variousembodiments of the present disclosure.

FIG. 2 shows a system for performing motion analysis in a field ofinterest, in accordance with some embodiments.

FIG. 3 shows a system for performing motion analysis in a field ofinterest, in accordance with some embodiments.

FIG. 4 shows a system for performing motion analysis in a field ofinterest, in accordance with some embodiments.

FIG. 5 shows a system for performing motion analysis in a field ofinterest, in accordance with some embodiments.

FIG. 6 shows a Motion-Intelligent Field (Indoor/Outdoor Applications),in accordance with some embodiments.

FIG. 7 show a Motion-Intelligent Field (Open Field Applications), inaccordance with some embodiments.

FIG. 8 shows Motion sensor Functions, in accordance with someembodiments.

FIG. 9 shows a Photodetector Sample, in accordance with someembodiments.

FIG. 10 shows motion sensor shapes and photodetector distribution, inaccordance with some embodiments.

FIG. 11 shows Motion Sensors in Buildings, in accordance with someembodiments.

FIG. 12 shows tiling with motion sensors and sensor resolution, inaccordance with some embodiments.

FIG. 13 shows three major components of artificial intelligencesoftware, in accordance with some embodiments.

FIG. 14 shows a velocity plane in the Fourier domain (Morlet wavelet),in accordance with some embodiments.

FIG. 15 shows synthetized video sequence, in accordance with someembodiments.

FIG. 16 shows a velocity plane in the Fourier domain (spatialfrequencies), in accordance with some embodiments.

FIG. 17 shows an adaptive dual control scheme, in accordance with someembodiments.

FIG. 18 shows an adaptive dual control in artificial intelligence, inaccordance with some embodiments.

FIG. 19 shows uncertainty principle in the photo-detector field of view,in accordance with some embodiments.

FIG. 20 is a block diagram of a computing device for implementing themethods disclosed herein, in accordance with some embodiments.

DETAILED DESCRIPTION

As a preliminary matter, it will readily be understood by one havingordinary skill in the relevant art that the present disclosure has broadutility and application. As should be understood, any embodiment mayincorporate only one or a plurality of the above-disclosed aspects ofthe disclosure and may further incorporate only one or a plurality ofthe above-disclosed features. Furthermore, any embodiment discussed andidentified as being “preferred” is considered to be part of a best modecontemplated for carrying out the embodiments of the present disclosure.Other embodiments also may be discussed for additional illustrativepurposes in providing a full and enabling disclosure. Moreover, manyembodiments, such as adaptations, variations, modifications, andequivalent arrangements, will be implicitly disclosed by the embodimentsdescribed herein and fall within the scope of the present disclosure.

Accordingly, while embodiments are described herein in detail inrelation to one or more embodiments, it is to be understood that thisdisclosure is illustrative and exemplary of the present disclosure, andare made merely for the purposes of providing a full and enablingdisclosure. The detailed disclosure herein of one or more embodiments isnot intended, nor is to be construed, to limit the scope of patentprotection afforded in any claim of a patent issuing here from, whichscope is to be defined by the claims and the equivalents thereof. It isnot intended that the scope of patent protection be defined by readinginto any claim limitation found herein and/or issuing here from thatdoes not explicitly appear in the claim itself.

Thus, for example, any sequence(s) and/or temporal order of steps ofvarious processes or methods that are described herein are illustrativeand not restrictive. Accordingly, it should be understood that, althoughsteps of various processes or methods may be shown and described asbeing in a sequence or temporal order, the steps of any such processesor methods are not limited to being carried out in any particularsequence or order, absent an indication otherwise. Indeed, the steps insuch processes or methods generally may be carried out in variousdifferent sequences and orders while still falling within the scope ofthe present disclosure. Accordingly, it is intended that the scope ofpatent protection is to be defined by the issued claim(s) rather thanthe description set forth herein.

Additionally, it is important to note that each term used herein refersto that which an ordinary artisan would understand such term to meanbased on the contextual use of such term herein. To the extent that themeaning of a term used herein—as understood by the ordinary artisanbased on the contextual use of such term—differs in any way from anyparticular dictionary definition of such term, it is intended that themeaning of the term as understood by the ordinary artisan shouldprevail.

Furthermore, it is important to note that, as used herein, “a” and “an”each generally denotes “at least one,” but does not exclude a pluralityunless the contextual use dictates otherwise. When used herein to join alist of items, “or” denotes “at least one of the items,” but does notexclude a plurality of items of the list. Finally, when used herein tojoin a list of items, “and” denotes “all of the items of the list.”

The following detailed description refers to the accompanying drawings.Wherever possible, the same reference numbers are used in the drawingsand the following description to refer to the same or similar elements.While many embodiments of the disclosure may be described,modifications, adaptations, and other implementations are possible. Forexample, substitutions, additions, or modifications may be made to theelements illustrated in the drawings, and the methods described hereinmay be modified by substituting, reordering, or adding stages to thedisclosed methods. Accordingly, the following detailed description doesnot limit the disclosure. Instead, the proper scope of the disclosure isdefined by the claims found herein and/or issuing here from. The presentdisclosure contains headers. It should be understood that these headersare used as references and are not to be construed as limiting upon thesubjected matter disclosed under the header.

The present disclosure includes many aspects and features. Moreover,while many aspects and features relate to, and are described in thecontext of motion analysis in a field of interest, embodiments of thepresent disclosure are not limited to use only in this context.

In general, the method disclosed herein may be performed by one or morecomputing devices. For example, in some embodiments, the method may beperformed by a server computer in communication with one or more clientdevices over a communication network such as, for example, the Internet.In some other embodiments, the method may be performed by one or more ofat least one server computer, at least one client device, at least onenetwork device, at least one sensor and at least one actuator. Examplesof the one or more client devices and/or the server computer mayinclude, a desktop computer, a laptop computer, a tablet computer, apersonal digital assistant, a portable electronic device, a wearablecomputer, a smart phone, an Internet of Things (IoT) device, a smartelectrical appliance, a video game console, a rack server, asuper-computer, a mainframe computer, mini-computer, micro-computer, astorage server, an application server (e.g. a mail server, a web server,a real-time communication server, an FTP server, a virtual server, aproxy server, a DNS server etc.), a quantum computer, and so on.Further, one or more client devices and/or the server computer may beconfigured for executing a software application such as, for example,but not limited to, an operating system (e.g. Windows, Mac OS, Unix,Linux, Android, etc.) in order to provide a user interface (e.g. GUI,touch-screen based interface, voice based interface, gesture basedinterface etc.) for use by the one or more users and/or a networkinterface for communicating with other devices over a communicationnetwork. Accordingly, the server computer may include a processingdevice configured for performing data processing tasks such as, forexample, but not limited to, analyzing, identifying, determining,generating, transforming, calculating, computing, compressing,decompressing, encrypting, decrypting, scrambling, splitting, merging,interpolating, extrapolating, redacting, anonymizing, encoding anddecoding. Further, the server computer may include a communicationdevice configured for communicating with one or more external devices.The one or more external devices may include, for example, but are notlimited to, a client device, a third party database, public database, aprivate database and so on. Further, the communication device may beconfigured for communicating with the one or more external devices overone or more communication channels. Further, the one or morecommunication channels may include a wireless communication channeland/or a wired communication channel. Accordingly, the communicationdevice may be configured for performing one or more of transmitting andreceiving of information in electronic form. Further, the servercomputer may include a storage device configured for performing datastorage and/or data retrieval operations. In general, the storage devicemay be configured for providing reliable storage of digital information.Accordingly, in some embodiments, the storage device may be based ontechnologies such as, but not limited to, data compression, data backup,data redundancy, deduplication, error correction, data finger-printing,role based access control, and so on.

Further, one or more steps of the method disclosed herein may beinitiated, maintained, controlled and/or terminated based on a controlinput received from one or more devices operated by one or more userssuch as, for example, but not limited to, an end user, an admin, aservice provider, a service consumer, an agent, a broker and arepresentative thereof. Further, the user as defined herein may refer toa human, an animal or an artificially intelligent being in any state ofexistence, unless stated otherwise, elsewhere in the present disclosure.Further, in some embodiments, the one or more users may be required tosuccessfully perform authentication in order for the control input to beeffective. In general, a user of the one or more users may performauthentication based on the possession of a secret human readable secretdata (e.g. username, password, passphrase, PIN, secret question, secretanswer etc.) and/or possession of a machine readable secret data (e.g.encryption key, decryption key, bar codes, etc.) and/or or possession ofone or more embodied characteristics unique to the user (e.g. biometricvariables such as, but not limited to, fingerprint, palm-print, voicecharacteristics, behavioral characteristics, facial features, irispattern, heart rate variability, evoked potentials, brain waves, and soon) and/or possession of a unique device (e.g. a device with a uniquephysical and/or chemical and/or biological characteristic, a hardwaredevice with a unique serial number, a network device with a uniqueIP/MAC address, a telephone with a unique phone number, a smartcard withan authentication token stored thereupon, etc.). Accordingly, the one ormore steps of the method may include communicating (e.g. transmittingand/or receiving) with one or more sensor devices and/or one or moreactuators in order to perform authentication. For example, the one ormore steps may include receiving, using the communication device, thesecret human readable data from an input device such as, for example, akeyboard, a keypad, a touch-screen, a microphone, a camera and so on.Likewise, the one or more steps may include receiving, using thecommunication device, the one or more embodied characteristics from oneor more biometric sensors.

Further, one or more steps of the method may be automatically initiated,maintained and/or terminated based on one or more predefined conditions.In an instance, the one or more predefined conditions may be based onone or more contextual variables. In general, the one or more contextualvariables may represent a condition relevant to the performance of theone or more steps of the method. The one or more contextual variablesmay include, for example, but are not limited to, location, time,identity of a user associated with a device (e.g. the server computer, aclient device etc.) corresponding to the performance of the one or moresteps, environmental variables (e.g. temperature, humidity, pressure,wind speed, lighting, sound, etc.) associated with a devicecorresponding to the performance of the one or more steps, physicalstate and/or physiological state and/or psychological state of the user,physical state (e.g. motion, direction of motion, orientation, speed,velocity, acceleration, trajectory, etc.) of the device corresponding tothe performance of the one or more steps and/or semantic content of dataassociated with the one or more users. Accordingly, the one or moresteps may include communicating with one or more sensors and/or one ormore actuators associated with the one or more contextual variables. Forexample, the one or more sensors may include, but are not limited to, atiming device (e.g. a real-time clock), a location sensor (e.g. a GPSreceiver, a GLONASS receiver, an indoor location sensor etc.), abiometric sensor (e.g. a fingerprint sensor), an environmental variablesensor (e.g. temperature sensor, humidity sensor, pressure sensor, etc.)and a device state sensor (e.g. a power sensor, a voltage/currentsensor, a switch-state sensor, a usage sensor, etc. associated with thedevice corresponding to performance of the or more steps).

Further, the one or more steps of the method may be performed one ormore number of times. Additionally, the one or more steps may beperformed in any order other than as exemplarily disclosed herein,unless explicitly stated otherwise, elsewhere in the present disclosure.Further, two or more steps of the one or more steps may, in someembodiments, be simultaneously performed, at least in part. Further, insome embodiments, there may be one or more time gaps between performanceof any two steps of the one or more steps.

Further, in some embodiments, the one or more predefined conditions maybe specified by the one or more users. Accordingly, the one or moresteps may include receiving, using the communication device, the one ormore predefined conditions from one or more and devices operated by theone or more users. Further, the one or more predefined conditions may bestored in the storage device. Alternatively, and/or additionally, insome embodiments, the one or more predefined conditions may beautomatically determined, using the processing device, based onhistorical data corresponding to performance of the one or more steps.For example, the historical data may be collected, using the storagedevice, from a plurality of instances of performance of the method. Suchhistorical data may include performance actions (e.g. initiating,maintaining, interrupting, terminating, etc.) of the one or more stepsand/or the one or more contextual variables associated therewith.Further, machine learning may be performed on the historical data inorder to determine the one or more predefined conditions. For instance,machine learning on the historical data may determine a correlationbetween one or more contextual variables and performance of the one ormore steps of the method. Accordingly, the one or more predefinedconditions may be generated, using the processing device, based on thecorrelation.

Further, one or more steps of the method may be performed at one or morespatial locations. For instance, the method may be performed by aplurality of devices interconnected through a communication network.Accordingly, in an example, one or more steps of the method may beperformed by a server computer. Similarly, one or more steps of themethod may be performed by a client computer. Likewise, one or moresteps of the method may be performed by an intermediate entity such as,for example, a proxy server. For instance, one or more steps of themethod may be performed in a distributed fashion across the plurality ofdevices in order to meet one or more objectives. For example, oneobjective may be to provide load balancing between two or more devices.Another objective may be to restrict a location of one or more of aninput data, an output data and any intermediate data there betweencorresponding to one or more steps of the method. For example, in aclient-server environment, sensitive data corresponding to a user maynot be allowed to be transmitted to the server computer. Accordingly,one or more steps of the method operating on the sensitive data and/or aderivative thereof may be performed at the client device.

Overview

The disclosure describes motion-intelligent systems that may performmotion analysis, supervision and control on delimited field of interestout of the physical world. A field of interest may define athree-dimensional space and time space, referred by acronym “3D+T” to bemonitored. Examples of a field of interest may include commercial andbusiness premises, residential, public and administrative buildings,parking garages, transportation stations and undergrounds, airports,private properties/residences, city streets, and battlefield ofinterests. A field of interest may be categorized into three mainvarieties namely motion-intelligent buildings (in FIG. 6), cities, andinaccessible grounds (open field of interests in FIG. 7).

Further, motion analysis may include motion detection of movingpatterns, motion-oriented classification and selection on the detectedmoving patterns, estimation of kinematical parameters includingvelocity, position, scale and orientation, and prediction of thekinematical parameters. Further, motion analysis may include tracking tobuild trajectories of moving patterns of interest, detection, indicationand prediction of abnormalities, incidents, and accidents, and focusingon patterns of interest.

Motion analysis may be performed passively and actively by sensingelectromagnetic and/or acoustic waves which physical properties havebeen transformed by the moving objects. For instance, an operator mayhave actively spread motion sensors randomly over an entire physicalfield of interest, and motion sensors may be nodes located at the bottomof a networking system. The networking system can may be decomposed intothree major components and described. A set of different sensors maycapture motion, provide high resolution information, make precisemeasurements, tag moving patterns of interest and convert informationinto data to be transmitted. Further, a tree-structuredtelecommunication system may relay the data from the sensors to a datasink or gateway connecting to other means of communication. Further, aremote monitoring center may receive the data and perform themotion-intelligent supervision and control. The motion analysis may beperformed from digital signals captured from numerous sensorsdistributed in the field of interest. The sensors may include motionsensors (passive photodetectors) randomly spread in the field ofinterest to analyze and track motion throughout the field of interestthrough three spectral bands, namely the visible spectrum for opticalimaging, the near-infrared for chemical imaging and the mid-infrared forthermal imaging. Further, the sensors may include video cameras locatedon key locations or embarked in moving systems such as drones or robotsto provide high resolution images and videos for final patternrecognition. Further, the sensors may include Active motion-measurementdevices based on ultrasonic, microwave, or laser radars to provideprecise measurement of the kinematical parameters for tracking, approachand capture. Further, the sensors may include marking sensors (passivewalk-through detectors) standing on key spots as specialized sensorsdetecting radioactive, chemical and biological sources, and moving metalpieces. Marking sensors also include active devices such as activebadges to mark or label some moving patterns as an item of specialinterest entering in the field of interest, and specifically, to tracethe moving patterns in the field of interest. The motion sensors and thenetwork components involved in local telecommunications to routers maybe manufactured using innovative nano-technology and Tera-Hertzcommunications to implement a local Internet of Nano-Things. At theremote monitoring center, raw data may be reconciled and re-ordered intime and space on an updated topographic representation of both thefield of interest and the sensor locations originally acquired duringthe initial training phase. The motion analysis may be performed by aneural network functioning in an adaptive dual control process with twomain modes depending on the predictability or the unpredictability ofthe environment. Further, dual control may proceed with a deep learningprocess, or with an expert system. Further, the deep learning processmay relies on an intelligence learned through training and updatingphase from a big data source. The deep learning process may be fast andmay refer to empirical way of learning on the field of interest. Theexpert system is based on the accurate model of the mechanics in thefield of interest and the wave capture in the sensors. Further, theexpert processing process may be slow and may refer to rational way oflearning.

In situations of interest, the dual control may also proceed to a thirdmode that may lock control on specific patterns of interest. Further,human supervision may also allow a possibility to react and sent remotecontrolled mobile systems with embarked video-camera like drones orrobots on a key location of the field of interest. Under thosecircumstances, the remote monitoring center would be able to communicatedirectly with the mobile systems bypassing the network.

To yield an effective structure description, the motion-intelligentsystem may be subdivided into three components as presented in FIG. 6,namely the sensor layer (lowest physical layer responsible for thedetection and the measurement of kinematical parameters), which mayinclude different type of sensors as described above, thetelecommunication layer, which may transmit the collected information toa gateway or a data sink, and may include upper physical layer of thedetectors, the components responsible for carrier generation, modulationand frequency selection, the data link layer, and the network layer, thetransport layer (the Internet, radio or satellite communications) andthe application layer (the Cloud, workstations specialized in ArtificialIntelligence especially deep learning neural networks).

To provide some context on the invention, motion-intelligent systemsmimic the work performed by the human sensory systems spread on theskin. Adapted for the present application, the sensory system spans theentire physical field of interest. Motion-intelligent systemapplications perform a motion analysis, supervision and control thatfall in two modes of operation which are namely passive or active.

In passive schemes, motion analysis may be performed like a humanperception in the cortex that may perform as a supervisor of motion.Passive sensors may capture propagating waves that may be emitted froman external source, usually in the visible spectrum, and may bereflected by moving targets. Sensors may also capture waves that may beproduced by the moving object itself, for instance if the object isthermally warm or hot. An example of such a sensor is a thermal infraredcamera. In active schemes, the motion analysis may derive accuratemeasurements that may enable fine control and action on the environment.Active sensors may produce analyzing waves (acoustic, microwaves) in thefield of interest, collect the reflected waves, compute relativevelocities of the target from Doppler shift, and perform echolocationthrough phase difference and time delay.

In an active scheme, motion analysis may proceed up to a final lockedcontrol on the pattern of interest. The analysis may proceed throughthree successive phases including search phase proceeding with a largespectrum recognition, approach selecting a target or patterns ofinterest, and terminal phase capturing or recognizing the pattern.

Further, intelligent-motion analysis and control based on a sensornetwork to be developed may work with biological sensory systems. Thesensory system may transduce signals in form of wave energy originatingfrom the physical world where motion may takes place into information.Only useful information is able to reach the brain through a gatewaywhere the information is analyzed by the cortex. Motion analysis isperformed by three different types of biological systems that performmotion analysis, supervision and control. The biological systems,including auditory systems, visual systems, and cutaneous sensorysystems provide perfect analogy to intelligent-motion control system tobe implemented. Further, each biological system is composed of threemain components including sensors located at periphery of the body inthe skin, nerves that work as a bundle or a network of “telephone” linesand transmit to the brain the useful information collected and filteredby the sensors, and, intelligent areas in the cerebral cortex that havelearned and acquired at an initial age both the topographic mapping ofthe body and the way how to generate a conscious perception of motion.

Auditory systems rely on ears as sensors and bring forth the opportunityto implement sonars and echolocation as rooted in bats and dolphins. Themotion analysis in the ears implements a time-frequency analysis whichis based on a continuous wavelet transform technique.

Visual systems rely on eyes as sensors. In human visual system,transmission network is based on a bundle of nerves that end up on twogateways in the brain located in the lateral geniculate nuclei. From thegeniculate nuclei, the information is spread and analyzed in the primaryvisual cortex. In the human eye, the information is split into twocomponents. A spot in the retina, called the fovea, createshigh-resolution images from a high-density photoreceptor grid thatenables visual recognition and classification. At the periphery of theretina around the fovea, a network of sparse photoreceptors is involvedin motion detection and tracking.

Cutaneous sensory systems rely on sensors, for example mechanoreceptors,non-uniformly spread over the entire skin. Further, some areas havehigher sensor density. The transmission network concentrate and bundlein the spinal cord. The sensory pathway synapses at the brain, proceedsto a gateway located in the thalamus. From the thalamus, the informationis spread into the brain to reach the cerebral cortex at the perfectlocation for conscious perception on a body map that was originallylearned.

Two competitive methodologies can be used for a “3D+T” intelligentmotion analysis, supervision and control of a field of interest. Motionanalysis performed may be from a set of numerous video camerasdistributed in the field of interest, also known as “camera-everywhere”approach. Further, motion analysis may be performed through motionsensors scattered in the field of interest and a restricted number ofvideo cameras located at selected spots. However, drawback of systemsbased on numerous video cameras are multi-fold. For instance, trends inconstructing video cameras may include moving to higher pixel density inorder to improve image resolution. Increasing the resolution diminishesthe sensitivity, which is needed to detect changes of contrast in anobserved scene especially in dim light. Move to high sensitivity maylead to use of detectors that may work each as independent pixel thatmay count photons. High sensitivity may require development of largefield of interests of view, which may diminishes resolution.

At telecommunication layer, each video camera may produces a compressedbit rate of several Megabits per second (Mb/s) that may need to betransmitted in real time, or stored but not yet analyzed to detectmotion. For example, compressing HD video with original samplingresolution of 1920×1080 pixels using a MPEG4 standard with a constantframe rate of 24, 25 or 30 progressive images per second (image/s) maygenerate bitrates that range from 5,000 to 10,000 Kbit/s. File-size ofthe compressed video may range from about 400 MB to 750 MB (Mega Bytes)after 10 minutes and 6 times those amounts after one hour. Further, atapplication layer, all video information may need to be analyzed in realtime to unfold the embedded motion. Therefore, the “camera-everywhere”involves a huge amount of data required to be transmitted, which mayoverpower the telecommunication network, and, to be processed by theapplication layer that may be untraceable or unmanageable in real timefor an intelligent system.

To compare both approaches, consider a motion-detector composed of8×8=64 sensors, where each sensor may generate 12-bit samples. At achange of contrast, information may be estimated at maximum of about 1Kbit encoded data per second over a period when intensity varies.Accordingly, the local system may have to involve 10,000 sensorspermanently to reach a level of a video-camera data rate.

As a matter of comparison with nature, evolution has chosen to develop anetwork of sensory systems that are composed of different specializedmotion sensors spread at the body periphery on the skin. The sensordensity is variable and locally adapted to the necessity or the need. Anetwork of nerves communicates the useful information to the cortexthrough a telephone line system bundled in the spine. The usefulinformation reaches the cortex after passing through a gateway thatrelays the signal to the centers of interest. In the cortex, thetransmitted signal produces a perception with intensity and localizationon the topographic map of the acquired body representation.

Motion detection is performed in the eyes at the periphery of the retinathrough a sparse system of photodetectors. The visual system orients theeyes and the fovea to the sensitized skin spot or towards the detectedmotion to get a high-resolute image of the pattern of concern. The humandetection system is based on multiple specialized sensor networks, oneintegrated eye, and a multi-brain where specialized and optimaldetection relies on networks of scattered sensors, specialized highlyresolution images relies on one single visual system, and a specializedpattern analysis and recognition supervision and control relies on thecortex which performs as a multi-brain.

The human detection system is more efficient as the human detectionsystem minimizes a quantity of information to be transmitted and to behandled by the cortex, and, the human detection system relies ondifferent contributing functions each optimally designed for a purpose.Restated in other words, design of a human body with eyes everywherewould lead to an inefficient and intractable system which would requesta bundle of high data rate transmission line and would flood the cortexof information. In the cortex, each source would request its ownspecific processing system to extract the useful content.

The motion-intelligent system mimics the functioning of a generalizedcentral and peripheral nervous system where each part may perform workwith optimum efficiency. The motion information may be captured by a mixof three categories of sensory systems each specialized for a knownpurpose, namely cutaneous sensory system (the motion sensor network),the visual system (the video-cameras) and the auditory system (theecholocation and radars). Network of communication may transport theinformation and reach an intelligent cortex through routers and onegateway. An artificial intelligence which may have originally acquiredthe topography of the field of interest may perform motion analysis. Oneanalysis may be performed experimentally bottom-up and a second analysismay be performed rationalistically top-down on-field of interesttraining and updating as a Q-learning system generating fast unconsciousperception of motion, and on computations performed by an expert systembased on actual physics of all the phenomena taking place in the fieldof interest (mechanics, waves and sensors) generating a slow consciousperception of motion. Moreover, the theoretical model with mechanics andwavelets may be universal and may apply for each sensory system fordetection, prediction and tracking. Further, the motion-intelligentsystem may detect any motion, predict a path, target and insulate anymoving patterns up to capture. The motion-intelligent system may beproactive on predicting incidents and accidents, which is where big datastreams and data analytics may reach optimal performances. Further, themotion-intelligent system may be scalable and fault resistant. A densityof sensors, volume for information storage and the computing power maybe each be individually increased. Existence of a universal modeloriginating from physics may implies convergence to one single existingoptimal solution for each field of interest configuration. The resultingsystem may have a capability to be stronger than any human or group ofhumans in terms of supervision and control and in term of preventingintrusions, providing security. Further, the motion-intelligent systemuses photo detection based motion sensors that may work with synergy inthree adjacent spectral bandwidths, namely visible light, near infraredand mid-infrared. Visible light may enable detection and the recognitionof patterns. Near infrared may enable the detection of moving or staticclouds of chemicals of interest. Mid infrared may enable detection andthe recognition of thermal activity, gunshots, fire and explosions.Further, the motion-intelligent system may activate, with humansupervision, another layer of communication by sending a robot or adrone to a site of interest. The robot or the drone may be able tocommunicate directly to the sensors or to a local sub-router on thefield of interest and directly to the remote monitoring center bypassingthe entire network of communication for fast action purpose. Further,the motion-intelligent system may be energy efficient. Sensing andmeasurement architecture may use a minimal level of energy and may usestate-of-the-art low-power sensing, amplification, and telecommunicationtechnologies. The motion-intelligent system may be discretely connectedto a power source or have advanced capabilities to harvest energy eitherinside buildings collected from ambient energy like energy radiated byelectromagnetic waves or outside buildings from energy collected bysmall solar panels. Sensors may be environmentally friendly. Further,the motion-intelligent system may offer a broad range of measurementsand short term and long-term statistics that may just limited by humanimagination and that may be increasing following progression of thetechnology especially the computing power. Further, themotion-intelligent system may offer ease of installation. Compared toexisting systems like camera, walk-through detector, themotion-intelligent system may need minimal installation effort. For eachmeasurement point, the motion-intelligent system may require to installwireless motion sensors on existing structures. Further, themotion-intelligent system may offer endurance as the sensors may notrequire batteries. The motion-intelligent system may need maintenanceafter installation related to training evaluation and situation updatesthat may not request operations to be stopped. The motion-intelligentsystem may have a long-life expectancy. Further, the motion-intelligentsystem may be almost invisible to the human eye making difficult to bedismantled. Therefore, the motion-intelligent system may not bevulnerable like video-cameras, walk-through detector, and existingoccupancy detectors.

Further, the motion-intelligent system may merge all existing motionsensors into a unique network that may connect to one single artificialintelligence. Further, the motion-intelligent system may use specificsensors that may each be specialized in a task making themotion-intelligent system efficient and effective in terms of theinformation that is transported over the network. Motion sensors may bepassive and ubiquitous sensors based on photodetection conveying highsensitivity to changes of contrast in different useful spectral band butwith less resolution. Motion sensors may lead to a three-dimensionalperception of motion which may depend on density and location in thefield of interest. Further, video-cameras may be passive and localizedsensors based on photodetection conveying high resolution image withless sensitivity. Video-cameras may lead to a three-dimensionalperception of motion. Further, radar-sonar sensors may be based onactive and localized sensors that may provide ultimately precisemeasurements of kinematical parameters along with some echolocation.Further, the motion-intelligent system may be universal and adaptive toany field of interest by mix of sensors that may be managed.

Further, the motion-intelligent system may be scalable andfault-tolerant. Further, the motion-intelligent system may be overallextendable/stretchable or contractible/shrinkable by adding orsubtracting modules or subfield of interests at will. Further, themotion-intelligent system may be locally adjustable in density wheresensors may be added or removed without interrupting work of globalfunctions. Further, the motion-intelligent system may allow motion to bedetected everywhere in the field of interest in real time by the use ofmotion-specific motion sensors. The sensors may be activated fortransmission when motion may be detected. Compared to existing motionsensors which may be occupancy sensors, the motion sensors may provideenough detailed information for global recognition and kinematicalparameter estimation. Further, the motion-intelligent system may beoptimal relatively to installed power which may be determined byinstalled technologies for detection, transmission and computer power.Implementations may follow technology advances converging to an optimalsolution. Being based on an artificial intelligence and ubiquitoussensors, the motion-intelligent system may leads to surveillance,security solutions that may be above human capabilities. As an example,deep learning system may defeat world-wide champions on most difficultgames, the GO-game.

Further, the disclosure describes design of a motion-intelligent systemthat may perform motion analysis, supervision and control from digitalsignal captured from a network of motion sensors scattered over aphysical field of interest and from multiple video cameras where “3D+T”motion analysis may be performed. Motion analysis may include motiondetection, motion-based classification and recognition of movingpatterns, and estimation, prediction and tracking of kinematicalparameters to build trajectories. Recognition and classification ofmoving pattern may include a selection through scale and orientation.Shape recognition may involve size, volume and shape. Orientationrecognition may involve perception of main alignment like horizontal,vertical, degree of inclination. Further, kinematical parameters may bedefined as spatial and temporal position and velocity or speed. Further,velocity may be vector with three components and the speed may bedefined as the magnitude of the velocity vector. The contribution ofvideo cameras may be to provide the motion-intelligent system withhigh-resolution images at locations that may be crucial for recognitionand classification of moving patterns. Further, the contribution of themotion sensor network may be to bring motion detection, estimation andtracking capabilities. For instance, if an operator has actively spreadmotion sensors randomly over an entire physical field of interest, theentire motion-intelligent system may be described following a bottom-upapproach and decomposed into three major components as introducedearlier in FIG. 6. Those components are as follows:

-   -   A set of different sensors captures motion, measurement and        moving-image information, converts them into data to be        transmitted.    -   A tree-structured telecommunication system relays the data from        the sensors to a data sink.    -   A motion-intelligent supervising system receives the data.

The motion sensors are nodes located at the bottom of the entirenetworking system. The following proceeds to a detailed bottom-updescription of the system.

The sensor nodes of the present invention implement all the functions ofthe physical layer of the system. Those functions are responsible forsignal detection, analog-to-digital conversion, entropy coding of theuseful information into data to be transmitted with potential errorcorrecting codes and encryption. The node uses an appropriate carrierfrequency and an efficient modulation technique.

The number of motion sensor nodes in the network is supposed to be veryhigh. A network may count a few hundred thousand to millions of motionsensor nodes. Two important properties and factor driving the design ofmotion-intelligent sensor networks shall be fault tolerance andscalability. Those characteristics shall serve as guideline to design aprotocol of communications inside the network.

Fault tolerance supposes that some sensor may fail to work momentarilyby lack of power of permanently by enduring physical damage. The failureof sensor nodes shall not affect the overall task of the sensor network.By definition, fault tolerance is the ability to maintain sensor networkfunctionalities without any interruption due to sensor node failures.The survival probability of a node, meaning the probability not to havea failure, within a time interval (0, t) is given in whole generality bya Poisson processP _(k) =e ^(−kt)  (1)

where λ_(k) is the failure arrival rate for a sensor node k and t is thetime period. Failure can also occur by cluster when a router located ata network node is failing or by any other means of subfield of interestdestruction.

The scalability is relating to the fact that density of sensor isscalable and can vary from region to region from a few sensors nodes insome areas to a few hundred of sensor nodes in some other areas. Thedensity can be calculated following the formulaμ(R)=(NπR ²)/A  (2)

where N is the number of scattered sensor nodes in area A, R is theradio transmission range.

The telecommunication network of the present invention has ahierarchical structure bottom up on the physical layer connectingsensors to sub-routers, a hierarchy of sub routers connects to routers,and the layer of routers connect to one gateway at the top of the treestructure. The structured telecommunication network implements the datalink layer and the network layer of the system. The data link layer isresponsible to establish the communication links for the data transferfollowing an infrastructure of multi-hop wireless communications, toensure reliable point-to-point or point-to-multipoint communications, tomultiplex or aggregate the data collected from the sensors, toeffectively share the telecommunication resources on the basis time,energy and frequency. The network layer is responsible to aggregate allthe data potentially using additional intermediate nodes as relays andto eventually route the total information to a data sink (the gateway)located at the periphery outside the sensor field of interest. Thearchitecture of this telecommunication network shall adapt to thespecific structure of the field of interest and its division intosubfield of interests. The physical field of interest can be decomposedor divided into a hierarchy of subfield of interests. Each subfield ofinterest corresponds to a specific area or section of the field ofinterest with its own properties, characteristics of interest. Eachsubfield of interest is controlled by one main router. Since a subfieldof interest can still be divided into smaller areas, each router cancontrol a set of sub-routers. Each router or sub-router has the abilityto perform networking functions that are more complicated than thoseperformed by the detector. Routers can be made of different technology,size and radio communication capabilities. All routers eventuallyconnect to one gateway which connects the entire system to a remotemonitoring center through another network (Internet, satellite, radio).The Internet or other built-up external networks constitute thetransport layer that connects the sink to the remote monitoring center.

The motion-intelligent supervising system located at a remote monitoringcenter manages the functionalities of the system. The remote monitoringcenter implements the application layer of the system. The incoming dataprovided by the gateways is processed in four major steps as follows:

-   -   1. The incoming data is reconciled and reconstructed in “3D+T”        on the acquired topography of the field of interest.    -   2. A deep learning artificial neural network supervised by an        expert system implements the motion analysis of detection,        recognition and classification of moving pattern including        abnormalities, incidents, and accidents.    -   3. A human supervision follows through to interpret all abnormal        events and give more insight to the system. The supervisor can        induce a top-down control forcing the system to up-date the        knowledge of the environment, to activate additional sensors        through routers, to involve video cameras moving with robots or        drones, to focalize and perform a locked control for pattern        recognition, measurement or capture.    -   4. A deep learning artificial neural network supervised by an        expert system performs additional prediction on the kinematical        parameters, data analytics, and trajectory construction.    -   5. All data are recorded and the systems can produce, on demand        in real time or delayed, all sorts of statistics performed on        different terms varying from real time, short terms hourly and        daily to long terms monthly and yearly.

The motion-intelligent system is based on a deep learning neuralnetwork. The deep learning system needs to be initially trained andevaluated. It also requests to be updated when changes occur in theenvironment. An adaptive dual control enables that the Q-learningfunction take actions from different sources as follows:

-   -   1. The deep leaning estimation that is trained and updated to        acquire the statistics of the environment, has learned and        updated its capability of detection, recognition and        classification, measurement and tracking.    -   2. The expert system computations based on both the actual model        of motion mechanics and the local topography of the system.    -   3. The precise measurements performed by active sensors in a        locked mode.    -   4. The supervisor decision.

At the remote monitoring center, the data originating from the gatewayare analyzed for detection, recognition and classification are presentedin real time to the supervisors. The supervisors have the possibility toselect moving patterns of interest to be tracked and captured by thevideo cameras. The system classifies all detected motions, classifiedthem by scale, shape and any other criteria, performs patternrecognition from the cameras, estimate the trajectories from the datacollected by the sensor system as far as it is feasible by a real-timeprocessing. All collected data are recorded to enable further off-lineanalyses and to perform statistics.

Once activated, each motion sensor communicates with a routerwirelessly. Each motion sensor encodes and transmits the innovativeinformation of the changes of contrast captured from the photodetectorarray at a pace requested by the environment changes. The transmitteddata are composed of sampled detector measurements in term of intensityand position entropy encoded for transmission, of time stamps, andsensor identification. In a usual setting, motion sensors are fixed onthe surfaces of construction buildings such as walls and ceilings. Themotion sensors capture moving light by photodetection. FIG. 9 shows themotion sensor network. In addition to the motion sensors, some othersensors shall or can be installed in the field of interest. Theseadditional sensors can be categorized as follows in a usual application:

1. A set of video cameras.

2. A set of passive sensors for specific detection and tagging.

3. A set of active sensors for precise motion measurements.

On the field of interest, a set of video cameras can be deployed on thefield of interest at key spots to catch high resolution images andvideos. All video cameras may transmit the video signals wirelesslythrough their related routers to reach the gateway which acts as thedata sink. At the data sink, the information is transferred through theInternet or another type of network or communications (like satellite)to the remote monitoring center. Additional passive sensors can bedeployed over the field of interest in limited number in the field ofinterest to detect critical information of interest like sounds andacoustics and moving patterns carrying radioactive sources,metal/weapon, or dangerous chemical. The detection may enable the systemto label or mark the moving patterns to trace its motion path, todetermine the location of entrance in the field of interest, to trackposition and velocity, and eventually, to allow recognition or capture.Additional active sensors may be deployed based on the use ofultrasounds, microwaves and lasers to perform complementary precisemeasurements of position and velocity as radars or echolocation assonars.

At the remote monitoring center, the raw incoming data provided by thegateways is processed in three major steps as follows:

-   -   1. The first step consists in a data reconciliation. Raw data        are reconciled and re-ordered by time and space. The algorithm        proceeds with a first stage of analysis which performs motion        detection and estimation performed from the sensors that are        active on the field of interest and with pattern classification        and recognition from video camera.    -   2. The system allows to receive human intervention at this stage        to give the ability to focus on events of interest.    -   3. The second step of analysis move further in the motion        analysis with motion prediction and trajectory estimation.

The three steps are reviewed with more details in the sequel.

Regarding the present invention's Data Reconciliation and InverseProblem, the first step consists in a data reconciliation to reconstructthe field of interest in “3D+” by fusing all the data originating fromall types of sensors and the video camera along with other datadescribing the topography of the field of interest. This stage involvesa process called inverse problem to detect and estimate motionparameters of interest from the data produced by the sensor networkfollowed by a process of pattern recognition and motion-basedclassification. The pattern recognition can be refined and/or completedfrom the data produced by the video cameras. The first step involves amotion analysis performed by a deep learning neural network and anexpert system. The deep learning neural network works and proceeds fromthe experience acquired during the training and updates which is abottom-up approach. The expert system works and proceeds from theaccurate models derived from the physics of mechanics and waves which isa top-down approach. The expert system operates in parallel to theneural network to implement an accurate model of motion as it takesplace in the field of interest taking into account the model of sensorsand of the field of interest topography. In this framework, the motiondetection and the estimations performed by the neural network aresupervised, controlled and potentially adjusted by the expert system.The deep learning neural network may proceed further to detect,recognize and characterize incidents, accidents, abnormalities of allkinds (behavioral, intrusion, fire, shots, explosions, etc.).

The deep learning neural network along with the expert system are ableto analyze the captured signals according to different motion parametersof interest. These motion parameters are defined as follows fromdifferent spatio-temporal transformations. The algorithm incorporatesthe following transformation parameters:

-   -   1. Spatial and temporal translations, with respective parameters        denoted by b∈R³ and τ∈R, provide the spatial and temporal        location.    -   2. Spatial rotation, with the parameter denoted yr∈SO(3), the        matrix of rotation in three-dimensions, provides the        orientation.    -   3. Spatial dilation, with non-zero positive parameter α∈        _(*) ⁺, provides the scale.    -   4. Velocity transformation with parameter v∈R³.

At this stage, a human supervision may be required to provide furtherinterpretation of some scenes. The human intervention further works toprovide a feedback on the system of video cameras to focus on areas ofinterest. At a most sophisticated level, the human intervention can userobots or drone to focus some camera on the site of interest. A feedbackon the sensor network can also be activated by requesting thatsub-routers activate more sensors in the area of interest or in areaswhere the inverse problem may require to be enhanced with a highersampling density. Such enhancement may be necessary to provide existing,unique and stable solutions for the current analysis under process.

The motion analysis is performed in two fundamental modes:

-   -   1. The use of an overall human supervision.    -   2. The use of a neural network implementing a deep learning        system working as a dual control.

The later mode enables to take decisions that are based on a Q-learningfunction. The Q-learning function further relies on an expert systemtaking rational actions, on a trained system taking empiric actions andon locked systems taking precise measurements.

The second step involves a motion analysis performed by a deep learningneural network in forms of a dual control system that predicts, tracksand constructs trajectories of interest. The process compares two ormore inputs and selects the optimal action to be taken by the Q-learningfunction. The first input is provided by an expert system like aconsciously calculated action (the rational action). The expert systemcomputes the kinematical parameters from exact models that rely on thetheoretical mechanics as it takes place on the field of interest and iscaptures by the sensors. The second input is the trained component whichcan be very fast since fully adapted like an unconscious nervous reflex(the empiric action)). It is produced by a neuro-dynamic programmingalgorithm following a statistical model learned by the system at fromthe initial and later trainings. At this stage, additional inputs mayalso be made accessible that originate from additional active motionsensors. Those sensors can be based on sonar or radar techniques(acoustics, microwaves or lasers) that perform accurate measurements onthe field of interest (the locked action).

In the inverse problem, detection and motion analysis are solved by adual control process functioning on a deep learning neural network andan expert system. The way a dual control implements an adaptive optimalcontrol is pictured in FIG. 17. On situation of interest, the algorithmcan freeze on specific patterns. Depending on the predictability or theunpredictability of the environment, the algorithm can make decisionsbased on two or more available chains of command.

Periods where the environment is predictable correspond to situationsthat have been learned during the training. On predictable situations,the deep learning algorithm can work as a stand-alone process that takesactions that rely to its training, meaning the training originallyreceived at the initiation of the system or the latest training update.During the training periods, the weights or the hyper-parameters of theneural network were computed and adjusted for optimal motion analysis.

On situations where the environment deviates from the acquiredstatistics and become unpredictable, the deep learning can take actionsthat refer to an exact model. The so-called expert system performs theoptimal motion analysis but at a lower speed. The deep learning systemneeds to be retrained or updated to the new environment statistics.

On special situations where the neural network can rely on additionalaccurate motion measurements made by an active system (like Dopplermeasurements through ultrasonic, microwave or laser systems), thesupervisor can freeze the control on the measurements performed by theactive system. Applications of a locked control can also be implementedas the capture by a robot of a pattern moving in the field of interest.The dual control system is sketched in FIG. 17.

The Q-learning function of the deep learning algorithm allows thataction be selected from different sources. In this application, anadaptive process is implemented in the actions to be taken can bedetermined following two control patterns which are:

1. A dual control.

2. A locked control.

The dual control differentiates between situations that are predictableto situations that are unpredictable. In a predictable environment wherethe model statistics are unchanged and correspond to the last trainingupdate, the action to be taken may follow and rely on the neural networksupervised by the expert system. In situations where the modelstatistics may have or have changed, the environment becomesunpredictable. Exercising caution and learning become the prevailingrules. The determination of the optimal action to be taken may bechanged by the supervisor in three different ways as follows:

1. Follow the action computed by the expert system.

2. Explore the new environment to learn.

3. Follow the action computed from another source of measurements.

The locked control corresponds to a possibility given to the supervisorto freeze on the system on a given target of interest. This option isespecially useful and efficient where active motion estimation isperformed through precise measurements using ultrasonic or laser systemsand can be entered as selected action.

FIG. 1 is an illustration of an online platform 100 consistent withvarious embodiments of the present disclosure. By way of non-limitingexample, the online platform 100 to facilitate motion analysis in afield of interest may be hosted on a centralized server 102, such as,for example, a cloud computing service. The centralized server 102 maycommunicate with other network entities, such as, for example, a mobiledevice 104 (such as a smartphone, a laptop, a tablet computer etc.),other electronic devices 106 (such as desktop computers, servercomputers etc.), databases 108, and sensors 110 over a communicationnetwork 114, such as, but not limited to, the Internet. Further, usersof the online platform 100 may include relevant parties such as, but notlimited to, end users, administrators, service providers, serviceconsumers and so on. Accordingly, in some instances, electronic devicesoperated by the one or more relevant parties may be in communicationwith the platform.

A user 116, such as the one or more relevant parties, may access onlineplatform 100 through a web based software application or browser. Theweb based software application may be embodied as, for example, but notbe limited to, a website, a web application, a desktop application, anda mobile application compatible with a computing device X00.

FIG. 2 shows a system 200 for performing motion analysis in a field ofinterest 214. Further, the system 200 may include a plurality of motionsensors 202A-B (such as motion sensor 202A and 202B) configured to bedisposed in the field of interest 214. Further, the plurality of motionsensors 202A-B may be configured to generate a plurality of motion datacorresponding to at least one motion of at least one object in the fieldof interest 214. Further, the system 200 may include a communicationdevice 204 configured for receiving configuration data associated withthe field of interest 214 from at least one data source. Further, thesystem 200 may include a processing device 206 configured for generatinga digital model corresponding to the field of interest 214 based on theconfiguration data using a simulation module 208. For instance, in someembodiments, the generating may include calibrating the digital modelbased on the configuration data. Further, the processing device 206 maybe configured for generating one or more of a plurality of motionsignatures corresponding to a plurality of predetermined motions and aplurality of object signatures corresponding to a plurality ofpredetermined objects based on the digital model using the simulationmodule 208.

Further, the processing device 206 may be configured for performingtraining of a deep Q-learning module 210 based on one or more of theplurality of motion signatures and the plurality of object signatures.Further, the processing device 206 may be configured for performing afirst analysis of the plurality of motion data based on the deepQ-learning module 210. Further, the processing device 206 may beconfigured for generating at least one trajectory data corresponding toat least one trajectory associated with the at least one object based onthe first analysis using the deep Q-learning module 210. Further, thesystem 200 may include a storage device 212 configured for storing thedigital model and one or more of the plurality of motion signatures andthe plurality of object signatures.

Further, in some embodiments, the system 200 may include a presentationdevice configured to present the digital model. Further, in someembodiments, the presentation device may include a display device.Further, in some embodiments, the presentation device may include atouchscreen display. Further, in some embodiments, the presentationdevice may include a sound reproduction device.

Further, in some embodiments, the digital model may include a visualrepresentation of the field of interest. Further, in some embodiments,the digital model may include a three-dimensional visual representationof the field of interest. Further, in some embodiments, the digitalmodel may include at least one digital representation of at least one ofthe plurality of motion sensors, at least one object in the field ofinterest, a plurality of light sources, a plurality of active sources, aplurality of video cameras, the at least one gateway and a topography ofthe field of interest.

Further, in some embodiments, the configuration data may include one ormore of at least one motion sensor characteristic, at least one objectcharacteristic, at least one light source characteristic, at least oneactive source characteristic, at least one gateway characteristic and atleast one field characteristic.

Further, in some embodiments, the digital model may include a motionsensor model associated with a motion sensor (such as the motion sensor202A) of the plurality of motion sensors 202A-B, an object modelassociated with an object of the at least one object, a light sourcemodel associated with a light source of the plurality of light sources,an active source model associated with an active source of the pluralityof active sources, a video camera model associated with a video cameraof the plurality of video cameras, a gateway model associated with agateway of the at least one gateway, a field of interest modelassociated with the field of interest 214 and a remote monitoring centermodel associated with a remote monitoring center.

Further, in some embodiments, the object model may include at least oneobject characteristic of the object. Further, in some embodiments, theat least one object characteristic may include a category of the object,a physical dimension of the object, a position of the object, anorientation of the object, a motion of the object, a visualcharacteristic of the object, a shape of the object, a color of theobject, a texture of the object, a weight of the object and a prioribehavior of the object.

Further, in some embodiments, the active source model may include atleast one active source characteristic of the active source. Further, insome embodiments, the at least one source characteristic may include atleast one of a type of the active source, a position of the activesource, an orientation of the active source, an intensity of the sourcewaves, a frequency of the source waves, a duty cycle of the activesource and a radiation pattern of the active source.

Further, in some embodiments, the gateway model may include at least onegateway characteristic of the gateway. Further, in some embodiments, thefield of interest model may include at least one field characteristic ofthe field of interest.

Further, in some embodiments, the processing device 206 may beconfigured for analyzing the at least one trajectory data based on atleast one predetermined rule. Further, the processing device 206 may beconfigured for identifying at least one event of interest based on theanalyzing of the at least one trajectory data.

Further, in some embodiments, performing training of the deep Q-learningmodule 210 may include generating the at least one predetermined rule.

Further, in some embodiments, the processing device 206 may beconfigured for activating at least one tracker based on identifying ofthe at least one event. Further, the at least one tracker may beconfigured for controlling at least one operational state of theplurality of motion sensors 202A-B in order to track the at least oneobject associated with the at least one event of interest.

In some embodiments, the digital model may include a three-dimensionalvisual representation of the field of interest 214. Further, the system200 may include a display device configured for displaying thethree-dimensional visual representation.

In some embodiments, the object model may include a plurality of objectmodels corresponding to a plurality of predetermined objects. Further, aplurality of object signatures may correspond to the plurality ofpredetermined objects. Further, the plurality of object signatures mayinclude a plurality of motion sensor data associated with the pluralityof motion sensors 202A-B. Further, the plurality of object models may bedetermined based on one or more of systematically varying the at leastone object characteristic and a strategic input received from an inputdevice operated by a human expert.

In some embodiments, the motion of the object model may include aplurality of predetermined motions. Further, a plurality of motionsignatures may correspond to the plurality of predetermined motions.Further, the plurality of motion signatures may include a plurality ofmotion sensor data associated with the plurality of motion sensors 202.

In some embodiments, the system 200 may further include a changedetection sensor configured to detect a change in the field of interest214 configured to detect. Further, the processing device 206 may beconfigured for triggering training of the deep Q-learning module 210based on one or more of the change and detection of an unpredictableevent associated with the at least one trajectory data.

In some embodiments, the motion sensor model may include at least onemotion sensor characteristic of the motion sensor 202A. Further, the atleast one motion sensor characteristic may include at least oneoperational characteristic. Further, the at least one operationalcharacteristic may include a type of the motion sensor 202A, asensitivity of the motion sensor 202A, a range of detection of themotion sensor 202A, an angle of aperture of the motion sensor 202A, aresolution of the motion sensor 202A, an accuracy of the motion sensor202A, a precision of the motion sensor 202A, a linearity of the motionsensor 202A and a time response of the motion sensor 202A. Further, theat least one motion sensor characteristic may include at least onedispositional characteristic. Further, the at least one dispositionalcharacteristic may include one or more of a position of the motionsensor 202A and an orientation of the motion sensor 202A. Further, atleast one of the range of detection, the orientation and the angle ofaperture may constitute a “field of view” corresponding to the motionsensor 202A.

In some embodiments, the light source model may include at least onelight source characteristic of the light source. Further, the at leastone light source characteristic may include one or more of a type oflight source, a position of the light source, an orientation of thelight source, an intensity of the light source, a duty cycle of thelight source, a spectral band of the light source, a color temperatureof the light source, a thermal spectral band associated with the lightsource (such as for e.g. an infrared radiator), a thermal spectral bandassociated with infrared sources, a radiation pattern of the lightsource and a range of illumination of the light source.

FIG. 3 shows a system 300 for performing motion analysis in a field ofinterest 214. The system 300 may include the plurality of motion sensors202A-B configured to be disposed in the field of interest 214.

Further, the system 300 may include the communication device 204configured for receiving configuration data associated with the field ofinterest 214 from at least one data source. Further, the system 300 mayinclude the processing device 206 configured for generating a digitalmodel corresponding to the field of interest 214 based on theconfiguration data using the simulation module 208.

Further, the system 300 may include the storage device 212 configuredfor storing the digital model and one or more of the plurality of motionsignatures and the plurality of object signatures.

In some embodiments, the processing device 206 may be further configuredfor performing a second analysis of the plurality of motion data basedon an expert system module 302. Further, the generating of the at leastone trajectory data may be based on the second analysis.

In some embodiments, performing the second analysis may includegenerating Galilei wavelets based on a plurality of kinematicparameters. Further, the Galilei wavelets may be group representationscomputed from extended Galilei groups. Further, the plurality ofkinematic parameters may be computed as spatio-temporal functionsdigitized in the space of the plurality of motion data. Further, theGalilei wavelets may facilitate analysis of the spatio-temporalfunctions transformed by motion. Further, the second analysis mayinclude estimating at least one kinematic parameter based on the Galileiwavelets. Further, the estimating may be performed using an inverseproblem technique based on a gradient algorithm with at least oneobjective function whose computation is based on the digitized Galileiwavelet transform. Further, the estimating of at least one motiontrajectory may be further performed by dynamic programming usingBellman's recursive techniques. Accordingly, a cost function may beoptimized using at least one Lagrangian function whose computation isbased on the digitized Galilei wavelet transform.

Further, the continuous wavelets may be representations of the extendedGalilei group in the space of the sensed signals (i.e. the plurality ofmotion data). Extension may be performed on the set of all the kinematicparameters which is composed of spatio-temporal location (space timeposition), dilation (scale), orientation, and velocity (all parametersof the analysis). Further, the inverse problem technique may be based ona gradient algorithm using an objective function to find the bestmatching parameter which is a best match filter and may be computed inspace-time domain in the norm of functions in the space of the kinematicparameters as the square of the inner product between the sensed signaland the analyzing Galilean wavelet. Further, the motion trajectorycomputation may be performed by dynamic programming through Bellman'srecursive equation using as cost function to be optimized as theLagrangian function computed in space-time domain in the norm offunctions in the space of the kinematic parameters as the square of theinner product between the sensed signal and the analyzing Galileanwavelet.

In some embodiments, the processing device 206 may be configured forperforming predictive analytics based on historical data associated withmotion analysis using the expert system module 302. Further, thegenerating of the at least one trajectory data may be based on thepredictive analytics.

In some embodiments, the performing of the second analysis of theplurality of motion data may be based on a physics model and a field ofinterest model.

In some embodiments, performing the second analysis of the plurality ofmotion data may be based on Lie group representations of motion andwaves as digitized continuous wavelets. Further, the generating of theat least one trajectory data may be performed as a filter matchingthough an inverse problem technique.

In some embodiments, the expert system module 302 may supervise andvalidate an output of the deep Q-learning module 210 based on anadaptive dual control. Further, in an unpredictable scenario, the expertsystem module 302 may perform one or more of training and updating ofthe deep Q-learning module 210 based on the second analysis.

FIG. 4 shows a system 400 for performing motion analysis in a field ofinterest 214. The system 400 may include the plurality of motion sensors202 configured to be disposed in the field of interest 214.

Further, the system 400 may include the communication device 204configured for receiving configuration data associated with the field ofinterest 214 from at least one data source. Further, the system 400 mayinclude the processing device 206 configured for generating a digitalmodel corresponding to the field of interest 214 based on theconfiguration data using the simulation module 208.

Further, the system 400 may include the storage device 212 configuredfor storing the digital model and one or more of the plurality of motionsignatures and the plurality of object signatures.

Further, the system 400 may include a plurality of video cameras 402A-Bdisposable at a plurality of key locations in the field of interest 214.Further, each video camera (such as the video camera 402A) may beconfigured to capture image sequences associated with a portion of thefield of interest 214. Further, at least one video camera (such as thevideo camera 402A) may be configured to transmit a part of acorresponding image sequence to a remote monitoring center 406 throughat least one gateway 404.

Further, the system 400 may include at least one gateway 404 disposableproximal to the field of interest 214. Further, the at least one gateway404 may be configured as a two-way interface capable of communicatingwith the remote monitoring center 406 and the plurality of motionsensors 202A-B. Further, the remote monitoring center 406 may includethe processing device 206. Further, the analyzing may be based on theimage sequences.

FIG. 5 shows a system 500 for performing motion analysis in a field ofinterest 214. The system 500 may include the plurality of motion sensors202A-B configured to be disposed in the field of interest 214.

Further, the system 500 may include the communication device 204configured for receiving configuration data associated with the field ofinterest 214 from at least one data source. Further, the system 500 mayinclude the processing device 206 configured for generating a digitalmodel corresponding to the field of interest 214 based on theconfiguration data using the simulation module 208.

Further, the system 500 may include the storage device 212 configuredfor storing the digital model and one or more of the plurality of motionsignatures and the plurality of object signatures.

In some embodiments, the system 500 may include a plurality of activesources 502A-B configured to emit source waves. Further, the pluralityof motion sensors 202A-B may be configured to receive reflected wavescorresponding to the source waves. Further, the plurality of motionsensors 202 may include one or more of a plurality of ultrasonic motionsensors and a plurality of microwave motion sensors. Additionally, insome embodiments, one or more of a plurality of ultrasonic motionsensors and a plurality of microwave motion sensors may be disposed at aplurality of key locations within the field of interest. Further, theprocessing device 206 may be configured for determining at least onecharacteristic difference between at least one source characteristicassociated with the source waves and at least one reflectedcharacteristic associated with the reflected waves. For example, in someembodiments, the at least one characteristic difference may include atleast one of a time difference, a shape difference, a durationdifference, an intensity difference and a frequency difference. Further,the processing device 206 may be configured for estimating at least onekinematic parameter associated with the at least one object in the fieldof interest 214 based on the at least one characteristic difference.

In some embodiments, the communication device 204 may be furtherconfigured for receiving a plurality of commands from at least onegateway communicatively coupled with the communication device 204.Further, the plurality of active sources 502A-B may be configured tooperate in one or more of a plurality of emission modes based on theplurality of commands. Further, an emission mode of the plurality ofemission modes may be characterized by one or more of a frequency ofemission, a length of emission, a delay interval between consecutiveemissions and a pattern of emission.

FIG. 6 show a motion-intelligent system that may be subdivided intothree components (and/or layers). First component may include a sensorlayer 602. Further, the sensor layer 602, in an instance, may be thelowest physical layer responsible for detection and measurement ofkinematical parameters. The sensor layer 602, in an instance, mayinclude different type of sensors such as specialty sensors 608, lasersensors 610, active motion sensors 612, microwave sensors 614, videocameras 632 (such as the video camera 402A and 402B), motion sensornetwork 616 etc. Further, second component may include atelecommunication layer 604. Further, the telecommunication layer 604,in an instance, may be in charge to transmit collected information to agateway 404 or a data sink. Further, the telecommunication layer 604, inan instance, may include an upper physical layer (such as a layer ofrouters (such as router 618), detectors, and/or components responsiblefor carrier generation, modulation and frequency selection etc.), a datalink layer (such as sub-routers 620), and/or a network layer (such assub-sub-routers 622). Further, third component may include anapplication layer 606, in an instance, may include a transport layer(the Internet, radio or satellite communications through an Ethernet624, a radio tower 626, and/or a satellite 628 respectively) and anapplication layer (the Cloud 630, workstations specialized in ArtificialIntelligence especially deep learning neural networks).

A general setting of the motion-intelligent system may be described asfollows. An operator may actively spread motion sensors (such as themotion sensor 202A and 202B) randomly in the field (such as the field ofinterest 214). Once released, each motion sensor communicates wirelesslywith a sub-router either in a single hop transmission or through otherneighboring sensors in a multi-hop transmission. Each motion sensor maytransmit a digital information composed of sampled measurementsoriginating from a photodetector array. Further, the data to betransmitted to the remote monitoring center 406 may at least contain asensor identification number with a time stamp, and digital samplesoriginating from the photodetectors, all digital samples may be entropycoded for transmission. Entropy coding may also imply that noinformation may be transmitted when no actual motion is detected. Thedata may be transmitted through sub-routers 620 to routers 618 andeventually reach a gateway (such as the gateway 404) to the Internet, toa local network, to a radio-communication system or a satellitecommunication. Each system aims to transport the aggregated informationto the remote monitoring center 406 where a computer performs the motionanalysis. In a regular setting, the motion sensors may be fixed onsurfaces of construction buildings such as vertical walls and/orhorizontal ceilings. Further, the motion sensors capture moving waves byphotodetection in spectral bands of the visible light, the near-infraredand the mid-infrared. Further, the motion sensor network 616 may beimplemented through different versions. Further, FIG. 6 presents amotion-intelligent field in an indoor/outdoor application. Further, FIG.7 presents a motion-intelligent open field which corresponds to a field(such as the field of interest 214) that may be temporarily inaccessiblefor environmental (for instance, by presence of radioactivity) ormilitary reasons (for instance, being located beyond enemy lines).

In a typical application like a building, a premise, a traffic orunderground tunnel, video cameras may be pre-positioned on key spots anda network of motion sensors may be arranged over the field of interest214, at best, on vertical outdoor structures, and on vertical andhorizontal indoor structures. Further, in a typical militaryapplication, some drones or robots (such as a drone 634 and a robot 636,as shown in FIG. 6) equipped with video cameras 632 and active motionmeasurement devices spread motion sensors (such as the motion sensor202A) as needed on an open field (such as the field of interest 214).The drone 634 (and/or the robot 636) may directly communicate with theremote monitoring center 406 and support several functions such asestablish direct radio-communications with the local sub-router on theopen field. Further, the drone 634 (and/or the robot 636) may beconfigured to locate positions of the active motion sensors 612 on thefield of interest 214 with following steps, such as, Illuminate motionsensors with coded infrared beams, Record the information of theparticular location as given by an embarked GPS, Receive the motionsensor identification through the local sub-router, and/or Transmit GPSlocation and corresponding motion sensor identification to the remotemonitoring center 406. Further, the drones (or robots) may transmitdirectly to the remote monitoring center 406 all data collected from thelocal motion sensor network 616, the data stream issued from the videocameras 632 and active measurement devices.

Further, the drone 634 (or the robot 636) may have an ability to moveand to focus video cameras 632 on targets of interest.

At the remote monitoring station 406, a raw incoming data provided bythe gateways (such as the gateway 404) may be processed in two-step. Thefirst step consists in a data reconciliation, and a reconstruction ofthe field in 3D by fusing all the data originating from the sensors, thecamera and other data describing the topography of the field of interest214. This stage may involve a so-called inverse problem to detect andestimate motion parameters of interest from the data produced by thesensor network and to perform classification and pattern recognitionadding the data produced by the video cameras 632. The first stepinvolves a motion analysis performed by a deep learning neural networkwhere detection and estimations may be supervised by an expert system.The expert system may implement an accurate model of motion as it takesplace in the field of interest 214, of sensors and of the fieldtopology. At this stage, other inputs may be introduced that originatefrom additional active sensors. Those sensors may be based on sonar orradar techniques (acoustic or laser) to perform accurate measurements orbased on detector techniques for chemical and radioactivity markingapplications. Human supervision may be required to interpret a scene.Further, a human intervention may work to provide a feedback on thesystem of video cameras 632 to focus on areas of interest. A feedback onthe motion sensor network 616 may also be activated to add new sensorsin areas of interest or in areas where the inverse problem may requireto be consolidated with a higher sampling density. Consolidation may benecessary to provide existing, unique and stable solutions to thecurrent process under analysis.

Further, the second step may involve a motion analysis performed by adeep learning neural network (such as the deep Q-learning module 210, asshown in FIG. 2) in forms of a dual control approach in order topredict, track and construct trajectories of interest. Further, analgorithm may compare two or more inputs to select the optimal action ofa Q-learning function. Further, one input may be provided by an expertsystem (such as the expert system module 302, as shown in FIG. 3)computing the motion control from models that rely on theoreticalmechanics. Further, a second input may be produced by a neuro-dynamicprogramming algorithm following the path learned by the system at fromthe previous training.

Further, the sensors, in an instance, may be classified in fourcategories. The video cameras 632, in an instance, may have the purposeto provide high resolution images and videos that enable to performpattern recognition and snapshots. Snapshots may enable to update andenlarge the data base of pattern to recognize. Further, the videocameras 632, in an instance, may be passive sensors that may beinstalled at key spots in the field. Further, the video cameras 632, inan instance, may be located at entrances and exits, at key passageway,and coupled with walk-through detectors and marking sensor meaninglocated at all spots where individual patterns may be singled out.Further, the video cameras 632 may be associated with each specificsubfield and connected to the corresponding sub-router 620 of the motionsensor network 616. The sub-router 620 may enable on and offtransmission of the video information to the remote monitoring center406 on the basis of the motion detected in its sub-field of control.Further, the video cameras 632, in an instance, may located in areas ofintense traffic that may concentrate groups of multiple patterns at thesame moment (such as large halls, transport platforms etc.) byopposition to areas of limited size (such as underground traffic tunnel,corridors etc.) where traffic may not be intense.

Further, the video information may be fused with the motion sensor datato perform the motion analysis at the remote monitoring center 406.Further, the video camera may be connected on sub-router 620 or routers618. The transmission of information from the video cameras 632 may beswitched on and off at the sub-router 620 (and/or the sub-sub routers622) function according to the moving activity detected by the motionsensors 202A in the subfield controlled by the sub-router 620. Thison-off switching may have a purpose to limit an amount of videoinformation propagating on the network and to make the system moreefficient.

Further, the video cameras 632 may also be embarked in moving systems(such as the drone 634, and/or the robot 636) that may have the abilityto move on demand to any spot of interest for perform closer and fasterobservations or actions. Further, the moving systems may be able toexchange information directly with the remote monitoring center 406 aswell as with the local sensors at least through the sub routers 620.Those direct telecommunications channels may be exterior to the sensornetwork.

Further, active motion measurement devices may be intended to detectmoving objects, conversations and sounds, and make precise measurementsof kinematical parameters. Further, the motion-intelligent system maydevelop techniques relevant to sonars and radars for echolocation. Thosesystems may be based on ultrasounds, lasers and microwave and computethe Doppler effect as the frequency shift between the emitted andreflected waves which is proportional to speed. Those systems are welldeveloped on the market. As a matter of fact, those sensors may beassociated with the video cameras 632 in the field (such as the field ofinterest 214) and embarked in the drone 634 or the robot 636 to performmore precise tracking and recognition. Each active sensor (such as theactive motion sensor 612) may be associated and communicating with asub-router (such as the sub-router 620).

Further, marking sensors may be specialized sensors made to labelindividuals, moving patterns or equipment's of interest. Marking sensorsmay be active or passive depending on whether or not they transmit asignal to motion detectors.

Further, Passive marking sensors (such as the specialty sensor 608) aretypically walk-through detectors that may detect the passage ofindividuals or a moving pattern that carry a special source ofradioactive, chemical or biological elements, that carry pieces of metalor any other abnormal or suspicious detectable items. Further, thepassive marking sensors may be coupled with video cameras 632 to record,picture and recognize the individuals. Once marked, the moving patternmay be traced all along its path in the field of interest 214. Further,the passive marking sensors may be installed at entrances and exits,gates or key passing corridors. Each passive marking sensor may beassociated and communicating with a sub-router.

Further, an active marking sensor may be a device that may produce asignal, electromagnetic wave, to be identified and detected by themotion sensors. Examples of active marking sensors may be active badgesor labels that provide a means of locating individuals, equipment andmoving patterns within a building by determining the location of theiractive badge. Active badges or label may produce an infrared signal witha limited infrared spectral bandwidth using an on-off modulationtechnique that may be destined to specific sensors included in themotion sensor. Several bands may be used according to different groupsof markers. Further, a message may contain a protocol of communicationand the useful information composed of a time stamp and anidentification number. Once received by a motion sensor (such as themotion sensor 202A), the information may be relayed with the sensoridentification and specific time stamp through the network to thegateway 404 and eventually sent to the remote monitoring center 406.Abnormal situations may be detected when the location detected by themotion sensor of the pattern carrying the active badge no longercorresponds to the position transmitted by the badge.

Further, each individual motion sensor may have a capability to performoperations as referred in FIG. 8. Accordingly, the operation may include(but not limited to) local digital processing (using central processingunit 804), clocking and time stamping (through clock/scheduler/timestamps 812), Memory storage or buffer management (by using temporarydata buffer 808), Photo-detection through an array of photodetectors802, Electromagnetic communications with a sub router or another sensor814, Nano-Power generation and Nano-batteries (using Nano-powergenerator and batteries 810). Further, additional functions may beimplemented such as Nano-GPS (not shown), and/or an Orientationmeasurement (not shown).

The motion sensors may be composed of an array of photodetector units(such as the array of photodetectors 802). Further, each photodetector(such as a photodetector 900) with angle of view 902 may be made of amicrolens 904 that may funnel the light to a substrate 906 made of up tonine hundred quantum dots 908 as shown in FIG. 9. Further, thePhotodetector 900 may mimic an insect ommatidium. The major challenge ofthe motion sensors may be posed by the very limited amount of energythat may be stored in nano-batteries, a situation which requires the useof energy-harvesting systems. Further, piezoelectric nano-generator havebeen recently proposed. Further, the sensor may need a memory buffer(such as the temporary data buffer 808). Further, the memory buffer maybe modeled by a queueing system. The queue size may be determined by themaximum number of data to be stored. A piece of information to be storedmay be made of a photodetection sample and the corresponding time stamp.The local digital processor feeds the memory buffer at a deterministicrate that corresponds to the sampling rate and the amount of dataproduced to the number of detectors. Further, an energy harvestingdevice generates energy by packets which arrival follows a model thatmay be described by a Poisson process. The resulting model is a queue offixed size, feed by a deterministic rate and emptied by a Poissonprocess with acronym D/M/1.

The motion sensors may be attached to permanent construction structureslike walls and ceilings. Both structures are available inside buildings,in tunnels for road traffic and in underground transportation. Thissetting allows to collect two projections of the motion which are namelyvertical with the walls and horizontal with the ceiling. The firstquestion is to determine the distance between two detectors or whatshould be their density on the structure. The best solution is toconsider the sensor angle of view and the distance to the oppositeparallel structure. For example, let us consider projections onhorizontal structures with detectors located on the ceiling. Eachdetector is characterized by a given field of view that ends up coveringon the opposite floor some area. Let us assume by symmetry that thislater area is in form of a disk. A disk is by definition a region on theplane of the floor limited or bounded by a circle. Let consider andrefer this disk under the generic name of a tile.

FIG. 11 shows an exemplary representation of the plurality of motionsensors 202A-D disposed on the at least one surface of an environment1114. For instance, the motion sensor 202A and 202C may be disposed at awall opposite to the wall 1102B in the environment 1114. Further, themotion sensor 202B and 202D may be disposed at the ceiling 1102A in anenvironment 1114.

Further, in some embodiments, the plurality of motion sensors 202A-D maybe associated with a plurality of field of views (such as a horizontalview 1106A, a vertical view 1106B). Further, a field of view of a motionsensor (such as the motion sensor 202A) may include a spatial region1104 within which a motion of an object may be detectable by the motionsensor 202A. Further, in some embodiments, the spatial region 1104 mayinclude a three dimensional region. Further, in some embodiments, thespatial region 1104 may include a one dimensional region. Further, insome embodiments, the spatial region 1104 may include a two dimensionalregion.

Further, in some embodiments, the environment 1114 may include a fieldof interest. Further, the field of interest defines a region of interestwithin which at least one motion event corresponding to at least oneobject may be detectable. Further, the field of interest (totalenvironment under monitoring) may be composed of a plurality of regionof interest (connected, disjointed, or, overlapping). Further, eachregion of interest may be comprised in one field of view or a plurality.Further, each region of the field of interest may be comprised in atleast one field of view of the plurality of field of views.

Further, in some embodiments, the spatial region 1104 may include athree dimensional conical region characterized by an apex pointcoincidental with a position of the motion sensor 202A, a height of thecone and a direction of the cone in relation to the at least one surface(such as a wall opposite to the wall 1102B) on which the motion sensor202A may be disposed. Further, in some embodiments, the direction of thecone is one of a vertical direction, a horizontal direction, and anangled direction.

Further, in some embodiments, the plurality of field of views (such asthe vertical view 1106B) may include at least two intersecting field ofviews (such as intersecting field of view 1110A and 1110B) characterizedby at least one overlapping region (such as an overlapping region 1108).Further, the at least two intersecting field of views (such as theintersecting field of view 1110A and 1110B) corresponds to at least twointersecting motion sensors (such as the motion sensor 202A and 202C) ofthe plurality of motion sensors 202A-202D. Further, a motion eventoccurring in the overlapping region 1108 may be detectable by each of atleast two intersecting motion sensors 202A and 202C.

Further, in some embodiments, the processing device 206 may beconfigured for determining a probability of failure associated with amotion sensor (such as the motion sensor 202A) of the at least twointersecting motion sensors 202A and 202C. Further, the processingdevice 206 may be configured for determining a number of the at leasttwo intersecting motion sensors (such as the intersecting motion sensors202A and 202C) based on the probability of failure. Further, theplurality of motion sensors 202A-D may include the number of the atleast two intersecting motion sensors 202A and 202C. Further, withreference to FIG. 12, the at least two intersecting motion sensors (suchas the motion sensor 202A and 202C) may be oriented (tilted) in a waysuch that the at least two intersecting field of views (such asintersecting field of view 1110A and 1110B) may result in a maximumoverlap 1202, or a critical overlap 1204, and/or a sparse overlap 1206.For instance, the maximum overlap 1202 may include the overlappingregion 1108 that may cover a maximum area. Further, in another instance,the critical overlap 1204 may include the at least two intersectingfield of views (such as intersecting field of view 1110A and 1110B)characterized without any overlapping region 1108. Further, in anotherinstance, the sparse overlap 1206 may include the at least twointersecting field of views (such as intersecting field of view 1110Aand 1110B) that may be placed at a significant distance from each otherwith no overlapping region 1108. Further, in some embodiments, aresolution associated with the intersecting field of view 1110A may bedetermined by the processing device 206, which may be dependent on anumber of photodetectors (such as a photodetector in the array 802)pilling-up in an array.

In a further embodiment, the arrangement of the motion sensor inbuildings are presented in FIG. 11 and similarly for tunnels. Let uscall by interval the distance between two consecutive detectors alongone axis x or along the perpendicular axis Y. The maximum tilingfrequency shall correspond to interval equal to half the tile diameter,i.e., the radius. Such overlap of several different aperture cones tocover motion enables the system to perform triangulations since themoving pattern is detected from different sensors at the same time. Moredensity would not bring more redundant information for less accuracy.Accuracy is also related to the detection resolution which is given bythe number of individual photodetectors that are inserted inside themotion sensor as presented in FIG. 12. Less density decreases theredundancy and the accuracy to locate the position. The critical tilingis reach when the interval between two consecutive detectors is equal tothe tile diameter. At critical tiling, each piece of floor is covered byonly one single detector, and for lower sensor density or longerintervals, there would be gaps between the tiles on the floor, andtherefore, gaps in the detection. The same situation exists on the wallsfor projections on vertical structures. But both walls can be coveredwith motion sensors leading to several possibilities, namely one wall,both walls, both with alternate position. Using both vertical andhorizontal projections, it is possible to build three-dimensional paths.

The resolution that is achieved for each motion sensor inside the angleof view depends on two variables, the number of individualphotodetectors actually inserted in the array of the motion sensor, and,the distance between the two horizontal or vertical structures thatdetermines the size of the tile.

The resulting projection of the photodetector field of view on the tiledetermines the size of the smallest details that can be detected andpositioned without any uncertainty. The field of view of a particulardetector is subject to an uncertainty relation for the simultaneousmeasurement of velocity and position when the moving pattern has a sizethat is below the resolution threshold. See addendum.

Motion sensor to be attached on vertical or horizontal structures arepresented in FIG. 10. Motion sensors for open field applications can bemade with a semilunar shape 1002 or a spherical shape 1004 equipped ofphotodetectors to cover 360 degrees on in all directions as presented inFIG. 10. Photodetectors can be implemented to mimic insect vision withthousands of individual photoreceptor units. Compound eyes possess avery large view angle, can detect fast motion, and in some cases,polarization of light. Moreover, insects can adapt to nocturnal visionand dimmed lights and cover the near infrared. Each motion sensors shallalso be equipped with some basic signal processing and informationstorage capabilities, nano-batteries and wireless communications.

The network communications, telecommunications, multi-hop among themotion sensors or single hop to the sub-routers, from sub-routers torouters and eventually to the gateway are not part of this descriptionand patent rights belong to others. The information to be transmitted iscomposed of a data transmission protocol followed by the sensoridentification number on 24 bits, a time stamp 24 bits and thecorresponding digitized photodetector samples which are readings holdingon 12 bits each, meaning n times 12 bits for n sensors in the array. Thebit rate out of a motion sensor would be a variable bit rate of entropycoding ranging from zero in quiet periods to one or a few Kilobits persecond during a peak traffic period. The resulting bit rate also dependsdirectly on the density of photodetectors that are implemented in themotion sensor. Simple error correction can be implemented as paritychecks. Information transmitted over the sensor network can be encryptedbut the actual protection of such punctual motion information is not acritical issue since just the remote monitoring center is able toreconcile all data with the topographic description of the field. Thedata that need to be protected are the final records derived for furtherstatistics after all monitoring work is performed.

At the remote monitoring center, the data transmitted from the gatewayare analyzed in real time for detection and classification and presentedto human supervisors. The supervisors have the possibility to selectmoving patterns of interest to be tracked and captured by video cameras.The system classifies all detected motions, by scale, shape, volume,velocity, orientation and other criteria introduced during the deeplearning neural network training. The system performs patternrecognition from the cameras, estimates trajectories from the datacollected by the sensor system as far as it is feasible by a real-timeprocessing. All collected data are recorded to enable further off-lineanalyses and to perform statistics.

The raw incoming data aggregated by the telecommunication network aresupplied by the gateway. The data are processed in two steps as follows:

-   -   1. The first step consists in a data reconciliation. Raw data        are reconciled and re-ordered in time and space on the        topographic representation of the field. The representation of        the field is acquired or introduced during the initial phase of        training of the system. The algorithm proceeds with a motion        detection and estimation performed from the different sensors in        the field and with pattern classification and recognition.    -   2. The second step proceeds further in the motion analysis with        motion prediction and trajectory estimation.

The algorithm is able to analyze the captured signals according todifferent kinematical parameters of interest. These kinematicalparameters are defined from different spatio-temporal transformations.The algorithm incorporates the following transformation parameters:

-   -   1. Spatial and temporal translations, respectively denoted by        b∈R^(n) and τ∈R, provide the spatial and temporal location.    -   2. Spatial rotation, with the matrix of rotation in        three-dimensions of which the parameter is denoted by r∈SO(3).        This parameter provides the orientation of the principal axis of        the pattern in term of two main directions being the horizontal        and the vertical or referring to the angle of deflection towards        those two main directions.    -   3. Spatial dilation, with the non-zero positive parameter α∈        _(*) ⁺ provides the scale.    -   4. Velocity transformation, with parameter v∈R^(n), provides the        velocity vector. The velocity not only includes the magnitude of        the vector defined as the speed, but also the vector orientation        through the components of velocity vector.

The first step consists in a data reconciliation and a reconstruction ofthe “3D+T” field by the fusion of the data originating from the sensorsand the video cameras with other data describing the topography of thefield. This stage involves a so-called inverse problem that computesestimates of the kinematical parameters of interest from the dataproduced by the sensor network. At this stage, a human intervention maybe required to interpret the scene. The human intervention further worksto provide a feedback on the system of video cameras in order to focuson areas of interest.

The algorithm implemented in this system is based on an inverse problemtechnique. An inverse problem is the technique that enables to computethe values of the parameters of physical transformations that take placein a field where the events are not directly observable. The inverseproblem is the mathematical process that consists of collecting data, inform of digital signals, from a sensor array in order to calculate thecausal parameters that have produced them. The causal parameters canonly be estimated if an accurate model of the transformations thatproduced them is known. The inverse problem technique enables theestimation and the analysis of structures that are located beyond thesensor network, and therefore, that are not accessible.

In this inverse problem, detection and motion analysis are solved by adual control process functioning on two main modes which are namely adeep learning neural network and an expert system. Those two modes canbe outlined as follows:

-   -   1. The deep learning process relies on an intelligence learned        by training, retraining and updating the system on the basis of        a big data source. This process refers to an empirical way of        learning also known as a bottom up approach and can be compared        to action routinely and/or unconsciously performed by the brain.    -   2. The expert system relies on a precise model of motion on the        field and the capture of electromagnetic waves by the motion        sensors to compute resulting kinematical estimates.        -   This process refers to a rational way of learning also known            as a top down approach and can be compared to educated and            conscious brain calculations.

On situation of interest, the dual control can also proceed to a thirdmode which freezes or locks the control on a specific pattern ofinterest. Depending on the predictability or the unpredictability of theenvironment, the dual control algorithm proceeds differently to makedecisions. Decisions can be based on two or more available chains ofaction command. The following describes three main ways to proceed:

-   -   1. Periods where the environment predictable corresponds to        situations that have been learned during the training. In        predictable situations, the deep learning algorithm can work        standalone and take actions that rely to its training, meaning        the training originally received during the initial learning        phase of the system or the latest training update. During those        training periods, the weights or the hyper parameters of the        neural network were computed for optimal motion analysis.    -   2. In situations that deviates from the statistics and become        unpredictable, the deep learning can take actions that refer to        an accurate model, the so-called expert system, which performs        the optimal motion analysis.    -   3. In special situations where the neural network can rely on        additional accurate motion measurements made by an active system        (like Doppler measurements through ultrasounds or laser system),        the supervisor can freeze the control on the measurements        performed by the active system.

The adaptive dual control system is sketched on FIG. 17.

The expert system algorithm performs a motion analysis on the data thatare collected. The motion analysis is based on the true and exact modelof the underlying physics and mechanics involved in the motion and thesensor units. The data that are collected are moving signals that aresampled from the motion sensor network and the video cameras. The movingsignals are spatio-temporal functions S (x, t) that belong to theHilbert space L² (R^(n)×R, d^(n)xdt) where x stand for thethree-dimensional spatial dimensions and t for the temporal dimension.In the scope of this algorithm, the moving signals can be parameterizedthrough kinematical transformation of which the parameters need to beestimated. It turns out that the motion parameters combine in analgebraic structure which can be identified as the element of a group Gwhich will refer to the Galilei group.

The motion model to be presented is based on the true theoreticalmechanics as it takes place in the field. The physics of mechanics andquantum mechanics is ruled by Lie groups. In this model, a Lie groupwill be presented which is the Galilei group that explains howkinematical parameters combine with each other to generate motion as itis performed in nature. Moreover, the theory developed for quantummechanics applies to classical mechanics. For example, it is possible tobuild functions in the functional space of the captured signals that arerepresentations of the Galilei group. Those representations can bedesigned as analyzing tools and will be called wavelets for the specialanalyzing properties they are endowed by mathematics. The analyzingwavelets used in this project are called Galilei wavelets. Galileiwavelets extend the concept of Eigen functions of eigenstate to theGalilei group G. The meaning is that Galilei wavelets extend theharmonic or Fourier analysis to functions transformed by the action ofmotion or that Galilei wavelets analyze functions in function spaceswhere transformations are ruled by the Galilei group. To outline, theexpert system computes the analyzing functions, so-called Galileiwavelets, in the space of the captured signals to estimate the value ofthe motion parameters. The analyzing functions used in the expert systemare group representations computed from the algebraic group G.

The next step proceeds with the description of how the expert systemdeploys this model based on the true physics and mechanics that takesplace on the field and in the detectors as a means to estimate thekinematical parameters in a technique called the inverse problem. Theresolution of the inverse problem is performed by an ascending gradientalgorithm on objective function and the sequel describes how toimplement in this algorithm to solve the inverse problem.

The theoretical mechanics method keeps on going by the construction oftrajectories which is based on the Euler-Lagrange equation andcorresponds to the extremum of a functional. As such the theory providesanalytical solutions to the problem of building trajectories. As a majorpoint, algorithms have been developed during the second part of the 20thcentury that build the path that optimizes the value of a function,called reward or cost function. As another point, those algorithms havecomputer implementations. The computational construction of trajectoriesrelies on the Bellman equations that founded dynamic programming where areward function is to be optimized over a long-term range. The basicconcepts of dynamic programming were originally prefigured by John vonNeumann, but Richard Bellman provided the final formalism. The recentincrease in computer power has enabled the implementation of thistechnique with neural networks.

For the Lie group of kinematical parameters, the motion analysisalgorithm implements an extended version of the group of physics calledthe Galilei group. The Galilei group is a Lie group defined in physicsthat describes the algebraic structure of the motion and wavepropagation transformations that takes place in the “3D+T” field. Thealgorithm of the expert system uses an extended version of the Galileigroup that adds two parameters, namely the scale and the orientation.For this reason, this extension is called the extended-Galilei group orthe affine-Galilei group. The resulting group combines all the usefulspace-time transformations into an operator Ω. When the operator Ω isapplied with specific parameter values on admissible functions, itgenerates an entire family or a set composed of an infinite number ofanalyzing functions. Each function is parameterized with the specificvalue introduced for kinematical parameters. This set of functionsenables to analyze the content of the captured signals according to anykinematical parameters. The resulting operator Ω that is used in thisalgorithm incorporates all the kinematical parameters and takes the formof the following matrix transformation:

$\begin{matrix}{{\Omega\left( {b,{\tau;v;a},r} \right)} = {\begin{pmatrix}{ar} & v & b \\0^{T} & 0 & \tau \\0^{T} & 0 & 1\end{pmatrix}.}} & (3)\end{matrix}$

acting on the column vector of spatio-temporal variables (x t 1)^(T).The set of the parameters associated to this operator Q formulate thealgebraic structure of a group G which generic element reads:G={g|g=(b,τ;v;a,r);b∈

^(n) ,τ∈

;v∈

^(n) ;a∈

_(*) ⁺ ,r∈SO(n)}  (4)

where the law of composition can be expressed from the matrixmultiplication:g∘g′=(b+arb′+r′v,τ+τ′;v+arv′;aa′,rr′)  (5)

This law of composition is associative but non-commutative as the resultof the isomorphism to the matrix multiplication. At this stage, eitherthe identity element or the inverse element needs still to be specifiedsince they imply each other. Accordingly, the identity element can bespecified as e=(0, 0; 0; 1, I₃) where I₃ is the three-dimensionalidentity matrix. The inverse element can then be computed from thematrix inverse and is given by:(b,τ;v;a,r)⁻¹=(a ⁻¹ r ⁻¹[τv−b],−τ;−a ⁻¹ r ⁻¹ v;a ⁻¹ ,r ⁻¹)  (6)

This law of composition defines a locally compact group which means thateach element has a neighborhood which closing is compact. Suchtopological property enables integration on the parameters. In thisgroup, two invariant measures can be defined as left and right invariantHaar measures respectively denoted here by d_(μl) and d_(μr). As anymeasure, both are as defined by the element of volume generated byinfinitesimal displacements applied on the group parameters. Therefore,

$\begin{matrix}\begin{matrix}{\mu_{l} = {{\det\;{\frac{\partial\left( {gog}^{\prime} \right)}{\partial g^{\prime}}}_{g^{\prime} = e}^{- 1}d^{n}b} ⩓ {d\;\tau} ⩓ {d^{n}v} ⩓ {da} ⩓ {dr}}} \\{= {a^{- {({{2n} + 1})}}d^{n}{bd}\;\tau\; d^{n}{vda}\;{dr}}}\end{matrix} & (7) \\\begin{matrix}{\mu_{l} = {{\det{\frac{\partial\left( {g^{\prime}{og}} \right)}{\partial g^{\prime}}}_{g^{\prime} = e}^{- 1}d^{n}b} ⩓ {d\;\tau} ⩓ {d^{n}v} ⩓ {da} ⩓ {dr}}} \\{= {a^{- 1}d^{n}{bd}\;\tau\; d^{n}{vda}\;{dr}}}\end{matrix} & (8)\end{matrix}$

where dr is the invariant measure on SO(n), and n=3. As the right andleft Haar measures are not equal, the group is called non-unimodular.Usual computations proceed to determine the corresponding Lie Algebra.Joint and adjoin action shall support the construction of theStone-von-Neumann representations in the Hilbert space of interest usingthe Mackey technique of orbit constructions.

In group representations, the operator {Ω: L²(R^(n)×R,d^(n)xdt)→L²(R^(n)×R, d^(n)xdt)} defined on the parameter set (b, τ; v;a, r)∈G generates the analyzing set of wavelets Ψ→Ω_(b,τ;v;a,rΨ). Theproperties that the representations must fulfill to define continuousspatio-temporal wavelets are the following triplet: unitary,square-integral able and irreducible. Group representations are derivedby this technique in the dual space L² (R^(n)×R, d^(n)kdω) which isequivalent to a Fourier space where k and co stand respectively for thespatial and temporal frequencies. In this section, the hat symbol isused above functions to represent their Fourier version and the barsymbol to represent their complex conjugate. The representations in theHilbert space are of the form:[Ω(g){circumflex over (Ψ)}](k,ω)=a ^(n/2) exp[i(k·b−ωτ)]{circumflex over(Ψ)}(k′,ω′)  (9)withk′=ar ⁻¹ kω′=ω−k·v  (10)

To fulfill the square-integrability condition, a candidate wavelet Ψ(k,ω) has to satisfy the following condition of admissibility meaning thatthere exists a finite constant C_(Ψ) such that:

$\begin{matrix}{C_{\Psi} = {{\left( {2\pi} \right)^{n + 1}\frac{{{\hat{\Psi}\left( {k,\omega} \right)}}^{2}}{{k}^{n}{\omega }}d^{n}k\mspace{11mu} d\;\omega} < \infty}} & (11)\end{matrix}$

meaning that the admissible function {circumflex over (Ψ)} is of finiteenergy or square-integral able over the entire space of the kinematicalparameters.

The analysis of the captured spatio-temporal signals S (x, t) isperformed as an inner product of the signals S(x, t) and the analyzingwavelet functions Ψ_(b,τ;v;a,r)(x, t) which reads:

$\begin{matrix}{\;{W\left\lbrack {{{S\left( {x,t} \right)};b}\;,{\tau;v;a},r} \right\rbrack}} & \; \\{= {C_{\Psi}^{{- 1}/2}\left\langle \Psi_{b,{\tau;v;a},r} \middle| S \right\rangle}} & (12) \\{= {C_{\Psi}^{{- 1}/2}d^{n}{xdt}\mspace{11mu}{\Psi\left\lbrack {{r^{- 1}\left( \frac{x - b - v}{a} \right)},{t - \tau}} \right\rbrack}\mspace{11mu}{S\left( {x,t} \right)}}} & (13) \\{= {C_{\Psi}^{{- 1}/2}d^{n}{kd}\;\omega\;{\overset{\overset{\_}{\hat{}}}{\Psi}\left( {{{ar}^{- 1}\overset{\rightarrow}{k}},{\omega - {k \cdot v}}} \right)}{\overset{\sim}{S}\left( {k,\omega} \right)}}} & (14)\end{matrix}$

Any wavelet {circumflex over (Ψ)} that fulfills the condition ofsquare-integrability will be a qualified analyzing tool for motionanalysis. The Morlet wavelet was used for the results derived in FIG.14. The design of the optimal analyzing wavelet depends on the problemto be solved.

To conclude, let us mention that an object which is put in motion with avelocity v preserves the spatial frequencies in the Fourier domain. Thespatial frequencies are shifted on a span given by the inner product(−v·k) along the temporal frequencies as presented in FIG. 16. Further,FIG. 15 shows synthetized video sequence.

This defines a velocity plane in the Fourier domain which is orthogonalto vector (v, 1), a plane of equation v·k+ω=0. The spectrum of all theobjects moving at velocity v will be concentrated along that planeinside some ellipsoid that accounts for some time-frequency Fourieruncertainty.

The inverse problem is the mathematical process of collecting a set ofobservations from a sensor array to calculate the causes that producedthem. Inverse problems are important mathematical processes since theyenable to compute the values of parameters that are not directlyobservable. The causal parameters can only be computed if an accuratemodel of the cause that produced them is known. For example, if thecauses are produced by waves, the model of wave propagation is a modelthat is known from the wave propagation equations and can lead toultimately precise computations. The inverse problem technique enablesthe estimation and the analysis of structures that are located beyondthe sensor network, and therefore, that are not accessible. If the modelis well-posed, it is possible to infer the exact parameter values. Butthe inverse model can be ill-conditioned depending on the positions ofthe sensors. A well-posed problem must satisfy three conditions:existence, uniqueness and stability of the solution. Depending on thenumber of sensors and their locations in the field, the second and thirdconditions may fail for some configurations.

Some well-known examples can be mentioned here. It is possible topicture the internal structure of the Earth by analyzing seismic wavescaptured from a sensor network located at the surface of the Earth.Astronomers are picturing the internal structure of the Sun by recordingthe vibrations of the surface of the Sun which are the results of shockwaves that propagate inside. Astronomers are recording the variations inthe cosmic microwave background to analyze the acoustic waves that werepropagating in the dense cloud of electrons and photons that existedafter the Big Bang. The cloud was so dense that it prohibited the lightto escape setting a barrier that limits our possibility to captureevents that took place closer to the Big Bang and before that clouddispersed. Solving this inverse problem with the model of the sonicshock waves that were propagating inside the cloud enables astronomersto collect explosion information that is closer to the Big Bang and ishidden by the cloud.

The inverse problem algorithm which is implemented in the expert systemhas as purpose to compute the best model parameters g* that fit to thedata d collected by the sensors. The purpose would be to find an inversemodel operator Π such that, at least approximately, the operator Πmatches exactly the captured data d for the best model parameters g*.That is:d=Π(g*)  (15)

In the context of the motion estimation, such an operator Π does notexist explicitly as described in Equation 15, and therefore, cannot bedirectly inverted to derive the best model parameters g*. Since theoperator Π cannot be directly inverted, an optimization method has to beused to solve the inverse problem. An objective function is thereforedefined to perform this optimization that will solve the inverseproblem. The objective function is a functional that measures how closethe data predicted from the model fits the observed data. In cases whereperfect data are collected without noise and where the appropriatephysics of the phenomena taking place is implemented in the model, therecovered data should fit the observed data perfectly. A standardobjective function, p, is usually of the form:ϕ=∥d−Π(g)∥₃ ²  (16)

meaning that the optimum is computed with the L²-norm or the Euclideandistance of the misfit between the observed data d and the predicteddata from the potential model Π(g). The optimization of the objectivefunction (i.e. solve the inverse problem) requires computing thegradient of the objective function in the parameter space. The gradientof the objective function is:∇_(m)ϕ=0  (17)

The optimization algorithm implemented in this system will take anotherform and lead to a gradient ascent algorithm for the reason thatfollows. Euclidean distance is the sum of squared differences,correlation is basically the average product. There is further a basicrelationship between the Euclidean distance and correlation. Let usexpress the correlation between two vectors x and y. An elementarycomputation shows that if x and y are both normalized, they will eachhave a mean of 0 and a standard deviation of 1, and therefore, thecorrelation denoted by r(., .) reduces to:

$\begin{matrix}{{r\left( {x,y} \right)} = {\frac{1}{n}{\sum\limits_{i}^{n}{x_{i}y_{i}}}}} & (18)\end{matrix}$

On the other end, if we expand the formula for the Euclidean distancedenoted by d(., .), we obtain:

$\begin{matrix}{{d\left( {x,y} \right)} = {\sqrt{\sum\limits_{i}^{n}\left( {x_{i} - y_{i}} \right)^{2}} = \sqrt{{\sum\limits_{i}^{n}x_{i}^{2}} + {\sum\limits_{i}^{n}y_{i}^{2}} - {2{\sum\limits_{i}^{n}{x_{i}y_{i}}}}}}} & (19)\end{matrix}$

But if x and y are both normalized, the sums Σ_(i) ^(n)x_(i) ² and Σ_(i)^(n)y_(i) ² are both equal to n and the product Σ_(i) ^(n)x_(i)y_(i)remains as the only non-constant term, a formalism which connects to thereduced formula for the correlation coefficient. In the case ofnormalized data, the relation between the correlation coefficient r andthe distance d reduces to:

$\begin{matrix}{{r\left( {x,y} \right)} = {1 - \frac{d^{2}\left( {x,y} \right)}{2n}}} & (20)\end{matrix}$

therefore, minimizing the Euclidean distance corresponds to maximizingthe correlation coefficient with an ascending gradient algorithm. Themaximum correlation technique is known in signal filtering as matchfilter. The correlation function used in this algorithm is thefunctional that computes the inner product between the captured signal Sand the analyzing wavelets. The analyzing tools are the waveletfunctions Ψ designed in the Hilbert space L² (R^(n)×R, d^(n)xdt) asadmissible representations of the Galilei group. Eventually, thealgorithm implements an objective function, φ, which is expressed in thespace-time domain as:ϕ(b,τ;v;a,r)=|

Ψ_(b,τ;v;a,r) |S

| ²  (21)

where the maximum is computed with the L²-norm in the functional spaceof the motion parameters. The algorithm implements a gradient ascent toderive the best matching parameters (b*, τ*; v*; a*, r*) as:(b*,τ*;v*;a*,r*)=arg max_((b,τ;v;a,r)∈G)ϕ(b,τ;v;a,r)  (22)

The evolution of a moving pattern defines a trajectory. FollowingLagrangian mechanics, the trajectory is derived by solvingEuler-Lagrange equation. The Euler-Lagrange equation is a differentialequation involving the functions b(τ) and its derivative b(τ) of thereal argument τ referring to the spatial position and the velocity bothfunctions of the time variable τ. The Euler-Lagrange equationcorresponds to a stationary point of a functional, called the action.This functional is defined as a time integral of a Lagrangian functionL:⊖(b)=∫_(a) ^(b) L[τ,b(τ),{dot over (b)}(τ)]dτ  (23)

The action is the integral of the Lagrangian from time t₁=a to time t₂=bthat generates a real number. The stationary point is derived from thefirst variation and reads as:∫_(a) ^(b) δL[τ,b(τ),{dot over (b)}(τ)]dτ  (24)

which is also known as Hamilton's principle or principle of the leastaction. At the stationary point, the Euler-Lagrange equation reads:

$\begin{matrix}{{{{\frac{\partial L}{\partial b_{i}}\left\lbrack {\tau,{b(\tau)},{\overset{.}{b}(\tau)}} \right\rbrack} - {\frac{d}{d\;\tau}{\frac{\partial L}{\partial b_{i}}\left\lbrack {\tau,{b(\tau)},{\overset{.}{b}(\tau)}} \right\rbrack}}} = 0}{{{{for}\mspace{14mu} i} = 1},\ldots\mspace{14mu},n}} & (25)\end{matrix}$

where L is the Lagrangian and Θ(b) is the trajectory defined by theextremum. The Euler-Lagrange equation is a necessary, but notsufficient, condition for an extremum of Θ(b). The functional Θ(b) has aminimum or a maximum at b=b* if its first variation δΘ(b)=0 at b=b* andits second variation δ²Θ(b) is strongly positive or negative at b=b*.Trajectories are described by the solutions of the Euler-Lagrangeequation for the action of the system. The Lagrangian approachsubstitutes the concept of mobiles accelerating in response to appliedforces to mobile moving on the path of a stationary action. This methodof representing motion and trajectories is more fundamental and enablesto connect with the wavelet representation of motion.

To proceed at this stage, the expert system needs to implement theLagrangian function and to define the algorithm to construct the motiontrajectories. In this expert system based on using wavelets as analyzingfunctions and the inner product as analyzing tool, the Lagrangianfunction is chosen to be the absolute value or modulus of the wavelettransform. The algorithm will compute the extremum in the L²-norm. Inthis setting, the Lagrangian reads:L[τ,b(τ),{dot over (b)}(τ)|a,r]=|{circumflex over (Ψ)}_((b,τ;v|a,r))|Ŝ)|² with {dot over (b)}(τ)=v  (26)

The construction of the motion trajectories is implemented with the useof dynamic programming theory based on the Bellman recursive equationswhere the Lagrangian function is destined to be the reward function. Forthe purpose to proceed to this algorithm of optimization, somerearrangements of the content of equation 26 need to be made as follows.The kinematical parameters, the analyzing function and the collecteddata need all to be redefined to fit to the concepts of action and stateas rooted in dynamic programming theory. The optimal {circumflex over(Ψ)} will derive the action to be taken at time τ, α_(τ) to build thenext piece of trajectory Θ(b) from the information of position (b, τ)and velocity v. The signal S stands for the signals sampled at time τthat produces a set of data collected at time τ. The set of datacollected at time τ will represent the state s_(τ) of the system at timeτ. The dynamic programming algorithm is a dynamic decision problem thateventually extends up to an infinite horizon. The sequence of alldecision is called the policy.

Let us define the state of the system at time τ to be s_(τ). A decisionsequence will start at time τ=0 from a given initial state to be s₀. Atany time τ, the set of possible actions depends on the current states_(τ). The action to be taken α_(τ) represents the control variables.The control variables are the variables to be chosen at any given timeτ. The potential number of actions to be taken belongs to a set Γ suchthat αt∈Γ(s_(τ)). The state changes from s_(τ) to a new state at timeτ+1 denoted s_(τ+1) where s_(τ+1)=T(s_(τ), α_(τ)) when action α_(τ) istaken. The resulting reward function from taking action ατ in states_(τ+1) is L(s_(τ), α_(τ)). Under these assumptions, an infinite-horizondynamic problem produces a total value function given by:

$\begin{matrix}{{V^{*}\left( s_{0} \right)} = {\max\limits_{{\{\alpha_{\tau}\}}_{\tau = 0}^{\infty}}{\sum\limits_{\tau = 0}^{\infty}{\gamma^{\tau}{L\left( {s_{\tau},\alpha_{\tau}} \right)}\mspace{31mu}{{with}:\;{0 \leq \gamma \leq 1}}}}}} & (27)\end{matrix}$

where:

1. V is the recursive value function.

2. γ is the survival likelihood of the trajectory.

3. α_(τ) is the action taken at time τ to build the trajectory Θ(b).

4. s_(τ) is the state of the system at time τ, corresponding to thecollected data.

The dynamic programming method breaks the decision-making problem intosmaller sub-problems as a result of Richard Bellman's principle ofoptimality which was stated as follows. An optimal policy has theproperty that whatever the initial state and initial decision are, theremaining decisions must constitute an optimal policy with regard to thestate resulting from the first decision. As stated in the principle ofoptimality, the first decision is considered separately, setting asideall future decisions. Therefore, starting at time τ=0, the best valueV-function, V*, reads:

$\begin{matrix}{{V^{*}\left( s_{0} \right)} = {\max\limits_{\alpha_{0}}{E_{s_{1}}\left\lfloor {{{L\left( {s_{0},\alpha_{0},s_{1}} \right)} + {\gamma\;{V^{*}\left( s_{1} \right)}}}❘s_{0}} \right\rfloor}}} & (28)\end{matrix}$

subject to the constraints: α₀∈Γ(s₀), s₁=T(s₀, α₀)

where E_(x) stands for the expected value or the mathematicalexpectation of the random variable x which is by definition the integral(or the sum in the discrete case) of the random variable with respect toits probability measure.

The entire dynamic problem can be rewritten in a recursive forminvolving the value function. Proceeding recursively step by step, wederive the equation, known as the Bellman's equation, expressing thebest value V-function, V*, reads at time τ as:

$\begin{matrix}{{V^{*}\left( s_{\tau} \right)} = {\max\limits_{\alpha_{\tau}}{E_{s_{\tau + 1}}\left\lbrack {{{L\left( {s_{\tau},\alpha_{\tau},s_{\tau + 1}} \right)} + {\gamma\;{V^{*}\left( s_{\tau + 1} \right)}}}❘s_{\tau}} \right\rbrack}}} & (29)\end{matrix}$

subject to the constraints: ατ∈Γ(s_(τ)), s_(τ)+1=T(s_(τ), α_(τ))

where:

-   -   1. V* corresponds to the best value function.    -   2. s_(tau) is the current state and s_(τ+1) is the future state.    -   3. T is the system transformation that assigns an existing new        state s_(τ+1) at time τ+1 from a state s_(τ) and an action a_(τ)        taken at time τ.    -   4. Γ(s_(τ)) is the set of all possible actions, α_(τ), that can        be taken from the state sτ at time τ.

As experienced in all deep learning applications on neural network, itis almost impossible to correctly guess the best choice of the weightsor hyper-parameters to be introduced in the neural network at the veryfirst time. Therefore, applied deep learning is a very iterative processthat requires to go around this cycle many times to hopefully find agood choice of network for the application. The data available fromsimulations and field experiments will be split in terms of a trainingset, a development or cross-validation set and test sets. The work flowis to keep on training algorithms on the training set, to use thehold-out cross-validation set to see which of many different modelsperforms best on this set. And after having performed this cycle enoughtimes to converge, a finalized best model of the neural network isreached that requires evaluation. The best model is evaluated on thetest set in order to get an unbiased estimate of how well the algorithmis performing. In the modern era of big data, it is a common practice toselect total set that may vary from 100,000 to one million examples intotal, then the trend is to have development test and a test set of one(1) percent of the total set. The learning process will be performed inseveral steps as follow:

-   -   1. The acquisition of the topography of the field of interest        which is a three-dimensional representation of the field entered        in the computer memory.    -   2. The localization of the motion sensors in the field which can        be achieved in two ways:        -   2.1. Rationally by measuring and recording the exact            positions of the motion sensors in the field at the time of            their installation.        -   2.2. Experimentally by passing a laser or light beam along            the surface of the field and detecting and recording from            the sensor network the information of the position in the            field that produces the maximum matching signal in the            sensor.    -   3. The calibration of the system for the kinematical parameters        which is performed in two ways:        -   3.1 Experimentally by a field training. Data are collected            by the sensor network by moving patterns of interest of            different size or scale, orientation and velocity with            reference to floor position markers. Different sources of            light shall be experimented with different position and            luminosity. The system will establish the direct correlation            between the pattern position, orientation and movement and            the corresponding sensor detection.        -   3.2. Rationally by building a 3D+T simulation on computer.            The system will implement and assemble the following pieces:            -   3.2.1. The three-dimensional field topography as                acquired as described in item #1.            -   3.2.2. The sensor locations as determined as in item #2.            -   3.2.3. The physical sensor characteristic of capturing                and transducing waves in information and data.

The simulation will run and add without restraint any made-up movingpatterns with different known size, orientation and velocity andmonitoring the sources of light in term of their position andluminosity. This procedure will not only train the deep learning neuralnet but also set up the expert system at an accurate running level.

Comparisons shall be established between the experimental resultsobtained in item #3.1. and the simulation results obtained in item #3.2.to adjust and/or correct the simulation model and the expert systemuntil proper correspondence is reached. Proper correspondence shall bespecified, but depends and is limited by the level of accuracy that ismaximally achievable by the implementation of the system.

-   -   4.1. The self-training of the neural net against the built-up        expert system which is calibrated to generate moving patterns        configured to the monitored field, to deduce the signals to be        collected by the sensor network in the field setting.

The presence of an expert system that can operate a training in arealistic manner enables the machine to work against itself and reach atremendously large training set.

A deep learning process will also perform an inverse problem from themotion sensor network and the video signals captured from multiplecameras, but in this case, it is learned by training, re-training andupdates. At this stage the neural network algorithm will detect themoving patterns, classify them according to scale, shapes, orientationvelocity, and position, pick up the pattern of interest and performrecognition following a pre-established database. The deep learningprocess will also detect the occurrence of abnormalities, detect andpredict incidents and accidents. All data will be available on computersthrough a menu.

To reach a formulation on the Q-learning system computing thekinematical parameters and deriving the trajectories, we need tointroduce the action-value function or Q-function which is a functionnot just conditioned to the current state s_(τ) but also to the actionα_(τ+1) that has been taken. The way to relate the value V-function withthe Q-function is as follows:

$\begin{matrix}{{V\left( s_{\tau} \right)} = {\max\limits_{\alpha_{\tau + 1}}{Q\left( {s_{\tau},\alpha_{\tau + 1}} \right)}}} & (30)\end{matrix}$

After taking their best value as V* and Q* and introducing them inBellman's equation #29, the result reads:

$\begin{matrix}{{V^{*}\left( s_{\tau} \right)} = {\max\limits_{\alpha_{\tau}}{E_{s_{\tau + 1}}\left\lbrack {{{L\left( {s_{\tau},\alpha_{\tau},s_{\tau + 1}} \right)} + {\gamma\;{\max\limits_{\alpha_{\tau + 1}}{Q^{*}\left( {s_{\tau + 1},\alpha_{\tau + 1}} \right)}}}}❘s_{\tau}} \right\rbrack}}} & (31)\end{matrix}$

But, by the definition given in Equation 30, the expected value on whichthe max_(ατ) is taken in Equation 31 is nothing but the best Q-function,Q*(s_(τ), α_(τ)), which read:

$\begin{matrix}{{Q^{*}\left( {s_{\tau},\alpha_{\tau}} \right)} = {E_{s_{\tau + 1}}\left\lbrack {{{{L\left( {s_{\tau},\alpha_{\tau},s_{\tau + 1}} \right)} + {\gamma\;{\max\limits_{\alpha_{\tau + 1}}{Q^{*}\left( {s_{\tau + 1},\alpha_{\tau + 1}} \right)}}}}❘s_{\tau}},\alpha_{\tau}} \right\rbrack}} & (32)\end{matrix}$

The result is similar to Bellman's equation but instead of considering astate, we consider the value of state coupled with an action. Theselected action is normally given by the best action as:α_(τ)*=arg max_(α) _(τ) Q(s _(τ),α_(τ))∈Γ(s _(τ))  (33)

meaning to proceed according to the following steps. From a particularsituation of the system at state sτ, the process successively optimizesthe Q-function over all possible actions, chooses the best action{circumflex over (α)}τ, applies the best action, reads the resultingstate s_(τ+1), captures the expected return, and finds the maximumexpected reward.

At this stage, more freedom of choice is provided to humans supervisingthe system as a result of the existence of an expert system. Theadaptive dual control enables to take other decisions in relation withthe environment. The action can be taken in different ways as follows:

-   1. The dual control first differentiates the options into two modes,    each of which the supervisor can choose. First, the choices are    between:

1.1. Controlling in situations or environments that are predictable,and,

1.2. Learning in situations or environments that are unpredictable.

Second, in some circumstances of interest, a third choice is given by:

-   2. Locking the control on a pattern of interest.

A schematic diagram of the adaptive dual control is presented in FIG.17. The equivalence of on adaptive dual control and an artificialintelligence based on an expert system and a Q-learning system ispresented in FIG. 18.

In a predictable environment where the statistical models are unchangedand correspond to the last training update, the action to be taken canfollow and rely on the neural network. This approach is the empiricalway of controlling based on experience which provides fast results. Thiscontrol can be compared to situations where the brain is taking decisionfrom learned and preprogrammed unconscious sets of actions. People oncetrained to bike in young age have never to learn to bike again.

In situations where the statistical models of the environment may haveor have changed, the environment becomes unpredictable, exercisingcaution and learning becomes the prevailing rules. Since the expertsystem is permanently supervising and checking the deep learning system,this situation happens for example when the expert system finds asignificant discrepancy between its computation result and those derivedfrom the neural net system. The determination of the optimal action maybe changed by the supervisor in two main ways as follows:

-   -   1. Follow the action computed from the expert system according        to the acquired topography of the field.    -   2. Explore the new environment and learn. During learning        periods, actions can be taken just to explore the environment,        not to maximize the Q-function necessarily. There are different        techniques that allow the system to decide which action to take        to explore the environment. One way to progress is to move with        probability ∈ to α*=arg max_(α′)Q(s,α′), and with probability        (1−∈), to make a draw out of a uniform probability distribution.

Following the accurate model provided by the expert system is therational way of controlling based on a model. The model is based ontheoretical mechanics and waves propagation and takes into account themotion sensors positions and detection characteristics. This process isslower than the empirical process since it requires more computerresources. This control can be compared to situations where the brain istaking decision from computing conscious sets of actions.

The locked control corresponds to a possibility given to the supervisorto freeze on the system on a given target of interest. This option isespecially useful and efficient where active motion estimation isperformed through precise measurements using ultrasonic, microwave orlaser systems and can be entered to take selected actions. The tools ofactive motion measurement can also be embarked with a video camera on adrone or a robot to supply detailed analysis leading to some capture orto perform more complex tasks or interventions.

Neuro-dynamic programing is the process that implements dynamicprogramming with a neural network. Neuro-dynamic programing works on thebasis of Q-learning. Q-learning is a model-free reinforcement learningtechnique where an action-value function, denoted by Q(s, α), is learnedfrom a training stage. Q-learning ultimately provides the expectedutility of taking a given action α in a given state s, thereafterfollowing the optimal policy. A policy is a rule that the agent followsby selecting actions, given a current state. When the action-valuefunction has been learned, the optimal policy can be constructed bysimply selecting the action with the highest value in each state. One ofthe strengths of Q-learning is that it is able to compare the expectedutility of the available actions without requiring a model of theenvironment as long as the environment is predictable. Q-learning canhandle any problems made of stochastic transitions and rewards.

The algorithm has a function that calculates the quality of astate-action combination as followsQ:(s×α)→R  (34)

By performing an action α∈Γ, the algorithm can move from one state toanother state. Executing an action in a specific state provides with areward L. The goal of the agent is to maximize the final recursive valuefunction over the entire span or horizon. It reaches this goal bylearning which action ατ is optimal for each state s_(τ).

Before learning has started, the Q-function is initialized to a possiblyarbitrary fixed value. Then, at each time τ the training selects anaction at and observes a reward function L_(τ) and a new state s_(τ+1)that may depend on both states s_(τ+1) and s_(τ+1) as well as on theselected action α_(τ), the Q-function is updated. The core of thealgorithm is a simple value iteration update, using the weighted averageof the old value and the new information as follows:

$\begin{matrix}\left. {Q\left( {s_{\tau},\alpha_{\tau}} \right)}\leftarrow{{\left( {1 - \beta} \right){Q\left( {s_{\tau},\alpha_{\tau}} \right)}} + {\beta\left\lbrack {{L\left( {s_{\tau},\alpha_{\tau},s_{\tau + 1}} \right)} + {\gamma\;{\max\limits_{\alpha_{\tau}}{Q^{*}\left( {s_{\tau + 1},\alpha_{\tau}} \right\rbrack}}}} \right.}} \right. & (35)\end{matrix}$

where β is the learning rate such that 0<β<1.

The implementation is made by a neuro-dynamic programming algorithmwhich is an approximation where the Q-learning function represents aneural network. The Q-function will now be parameterized with thekinematical parameters g=(b, τ; v; a, r) and Q becomes a function in theform of Q(s_(τ), α_(τ); g). The Q-functions are implemented as a neuralnetwork that takes states and actions as inputs and provides the bestaction to be performed as optimal output.

As the result of parameterizing Q with the g-parameters and implementingQ-function as a neural network, the computations of Q(s_(τ), α_(τ); g)are approximations of what would be computed with the actual Bellman'srecursive algorithm. The neural network implements an approximation ofthe actual dynamic programming algorithm. Therefore, an error or lossfunction needs to be computed which measures how far the neural networkstands from the actual Bellman's corresponding back-up. Eventually, theloss function L has to be minimized applying a gradient descentalgorithm which will derive the optimal parameters.

The algorithm computes the loss function L in the L²-norm as thedifference between the target produced by the true Bellman's recursivecomputation:E ₈ _(r+1) [L(s _(τ) ,a _(τ) ,s _(τ+1))+γ max_(a) _(r+1) Q*(s _(τ+1) ,a_(τ+1) ;g _(i−1))]

And the neural network Q(sτ, aτ; gi) as

$\begin{matrix}{{\mathcal{L}\left( {\mathcal{g}}_{i} \right)} = {E_{s_{\tau},\alpha_{\tau}}\left\{ \left( {{E_{s_{\tau + 1}}\begin{bmatrix}{{L\left( {s_{\tau},a_{\tau},s_{\tau + 1}} \right)} +} \\{\gamma\;{\max\limits_{\alpha_{\tau + 1}}{Q^{*}\left( {s_{\tau + 1},{a_{\tau + 1};{\mathcal{g}}_{i - 1}}} \right)}}}\end{bmatrix}} - {Q\left( {s_{\tau},{a_{\tau};{\mathcal{g}}_{i}}} \right)}} \right)^{2} \right\}}} & (36)\end{matrix}$

Let us remark that the target can only use the g parameters computedfrom the previous stage i−1 to induce a feedback correcting loop.

Taking the derivative of the loss function and using the chain rule, theresult reads in a gradient form as:

$\begin{matrix}{{\nabla_{{\mathcal{g}}_{i}}{\mathcal{L}\left( {\mathcal{g}}_{i} \right)}} = {E_{s_{\tau},a_{\tau}}\left\{ {\left( {{E_{s_{\tau + 1}}\left\lbrack {{L\left( {s_{\tau},a_{\tau},s_{\tau + 1}} \right)} + {\gamma\;{\max\limits_{\alpha_{\tau + 1}}{Q^{*}\left( {s_{\tau + 1},a_{{\tau + 1};{\mathcal{g}}_{i - 1}}} \right)}}}} \right\rbrack} - {Q\left( {s_{\tau},{a_{\tau};{\mathcal{g}}_{i}}} \right)}} \right){\nabla_{{\mathcal{g}}_{i}}{Q\left( {s_{\tau},a_{\tau},{\mathcal{g}}_{i}} \right)}}} \right\}}} & (37)\end{matrix}$

algorithm is performed to derive the optimal kinematical parameters ĝand finally and derives the best action to be taken as:α_(τ)*=arg max_(α) _(τ) Q(s _(τ),α_(τ) ;g*)∈Γ(s _(τ))  (38)

To design a reinforcement learning algorithm with a neural network, theaction is chosen from the Q-function where the parameter has beenoptimized, i.e., updated. The algorithm works as follows:

-   -   1. Start with a state s_(τ).    -   2. Find the optimal parameters g*.    -   3. Choose the best action to be taken α₁.    -   4. Observe the environment changing to state s_(τ+1).    -   5. Update the optimal parameters ĝ and move back in Item #3.

One of the major point about Q-learning algorithm is that the bestaction in Item #3 can be chosen as the optimal or can be chosen from amechanism that is different from the mechanism used to find the bestaction. Different alternative agents can provide alternative choices forthe best action. Action can also be taken from the following sources:

-   -   1. The expert system computations.    -   2. The accurate motion measurements performed by active devices.    -   3. The strategies to learn and/or explore an unknown        environment. A particular strategy has been explained earlier        through a way to progress with probability ∈ to α*=arg        max_(α′)Q(s, α′), and, to make a draw out of a uniform        probability distribution with probability (1−∈). The overall        strategy aims at learning Q, therefore, at taking actions that        explore ranges where Q is not well-known.

In the matrix formulation obtained to describe the transformationsinduced by the Galilei group, the mathematical formulation issued fromquantum mechanics still holds for any pair of non-commuting operators.Non-commuting operators represent observables which are subject tosimilar uncertainty limits. An eigenstate of an observable representsthe state of the analyzing wavelet function for a certain parametermeasurement value (the eigenvalue). For example, if a measurement of anobservable A is performed, then the system is in a particular eigenstate{circumflex over (Ψ)} of that observable. However, the particulareigenstate of the observable A needs not be an eigenstate of anotherobservable B. Then the observable B does not have a unique associatedparameter measurement for the observable A, as the system is not in aneigenstate of that observable B.

When a state is measured, it is projected onto an eigenstate in thebasis of the relevant observable. For example, if an object temporalposition τ is measured, then the state amounts to a temporal positioneigenstate. This means that the state is not a velocity v eigenstate,and it can but rather be represented as a sum of multiple velocity basiseigenstates. In other words, the velocity must be less precise. Thisprecision may be quantified by the use of their standard deviations:σ_(τ)=√{square root over (E(τ²)−E(τ)²)}  (39)σ_(υ)=√{square root over (E(υ²)−E(υ)²)}  (40)

where E(.) stands for the expected value. As in the wave mechanicsinterpretation provided here above, a tradeoff needs to exist betweenprecise measurements to be made on the respective parameters at the sametime. The result is ruled by an uncertainty principle.

For a pair of operators A and B, we can express their commutator [., .]as defined by:[A,B]=AB−BA  (41)

In this notation, the Robertson uncertainty relation keeps a form veryclose to the Heisenberg original inequality:σ_(A)σ_(B)≥½|E([A,B])|  (42)

This uncertainty relation combines two kinds of errors as follows:

-   -   1. The statistical error which is the inaccuracy of a        measurement of an observable A, and,    -   2. The systematic error component which is the disturbance        produced on a subsequent measurement of the variable B by the        former measurement of A.

If this uncertainty relation is applied to the non-commuting operatorsof temporal position and velocity, it follows from the matrixrepresentation of the Galilei group that:σ_(υ)σ_(τ)≥½|E([υτ′−υ′τ])|  (42)

which can be simplified without loss of generality by taking the initialtime τ=0, and writes as follows:

$\begin{matrix}{{\sigma_{v}\sigma_{\tau}} \geq \frac{{E\left( \left\lbrack {v\;\tau^{\prime}} \right\rbrack \right)}}{2}} & (44)\end{matrix}$

This inequality can be interpreted as the uncertainty created by theaperture cone or the field of view of a single detector, in any planeorthogonal to the principal cone axis as shown in FIG. 19. At any depth,the intersection of the cone and the orthogonal plane is a circle inwhich an uncertainty is created. This uncertainty situation is createdby the fact that the sensor is blind to any variations of motion thatare taking place in the cone section. If time is precisely measured, theuncertainty on the velocity corresponds to all the possible velocitiesthat the mobile will take to travel an expected distance equal to halfthe average length of a cord of the cone section during the precisemeasure of time. For example, if the intersection of the cone is acircle, if the radius is s, and all cords are uniformly distributed thenthe average cord length s given by

$\begin{matrix}{{E\left\lbrack {{v\;\tau}} \right\rbrack} = {{\frac{1}{\pi}{\int_{0}^{\pi}{2\; R\;\sin\;\frac{\phi}{2}d\;\phi}}} = {\frac{4R}{\pi}.}}} & \;\end{matrix}$The uncertainty principle certainly matters when dealing with smallscale sensors, but not really in the case of the high-resolution imagescaptured by video cameras for computer vision. Let us remark here that asecond uncertainty relation exists in the Fourier domain involving theparameters v and k which reads with normalization: σ_(v)σ_(k)≥½ as itcan be observed in FIG. 9.

The Artificial intelligence software of the application layer located inthe remote monitoring center will be implemented in local computers orbe addressed by connecting to the cloud through the Internet. Theartificial intelligence software may be composed of three (3) majorcomponents (shown in FIG. 13) which are as follows.

-   -   1. The simulation module 208.    -   2. The deep Q-learning module 210.    -   3. The expert system module 302.        The deep Q-learning module 210 and expert system module 302 both        interact with each other according to a dual control as        described earlier. The simulation module 208 is basically        connected to one single (huge) screen. To operate the system,        the human supervisor just needs to have one computer window to        connect directly to a local computer, or through the Internet to        a website where the cloud is accessible. The software gives        access to a menu leading to different operating modes. Figure X        provided here below sketches the interactions between the        different parts of this artificial intelligence system.

The Simulation Module 208

The simulation module 208 implements a mapping representation of thethree-dimensional field or environment to monitor taking into accountthe following characteristics.

-   -   1. the topography of the field (introduced from available maps        and in-site measurements).    -   2. the light sources (position, intensity and range of        irradiance variation, and illumination pattern).    -   3. the sensors (all kind in the field as included in the        monitoring system, position, physical models of capturing and        transforming irradiant energy into digital information).

In an initial stage, the simulation module 208 needs to be calibratedfrom the field in order to set up all the exact values of the set ofparameters described in items 1 to 3 here-above: positions andcharacteristics of all sensors and light sources. The calibrationproceeds further by a training where patterns of different scale andorientation are passed through the field and their signatures recordedat all different positions and velocities. This training process willsimilarly train the deep Q-learning module 210 and calibrate the expertsystem module 302.

Once correctly calibrated, the simulation module 208 can perform in twofollowing modes:

-   -   1. Simulation, meaning to generate/emulate virtual moving        objects in the field, computing the data that should be received        from the telecommunication network, infer their consequent        representations in space and time on the field representation,        display on the TV screen 1302 and feed the both the deep        Q-learning and Expert system module 302. Simulation        representations need to be confronted to the expert system        module 302 estimations to allow perfect matching and calibration        between simulation module 208 and expert system module 302. The        simulation module 208 can then proceed to train the Q-learning        system and the dual control first in term of all relevant        kinematic parameters and trajectories, and second, in term of        prediction of abnormalities, incidents or accidents. Training        and retraining occur before operations at the start of the        system, and during operations, at the occurrence of changes in        the environment and of unpredicted events. In this mode, moving        patterns are emulated, representations are created and displayed        on the screen in front of the supervisor. The deep Q-learning        keeps on training being supervised by the expert system module        302 in a dual control approach. Simulations can be produced        either by algorithms that explore randomly and        quasi-exhaustively all potential still unforeseen situations or        by human operations by enumerating all specific and strategic        situations that has a potential to occur.    -   2. Operation, meaning to represent and map on the field        representation all the information received and decoded in real        time from the telecommunication network. In this working mode,        all decoded information is communicated to both the deep        Q-learning and expert system module 302 working in dual control.        The real time processing performed by both Q-learning and exert        system in dual control will return the proper estimated values        of the relevant kinematic parameters, trajectories, and        eventually, the term of prediction of abnormalities, incidents        or accidents, all of which being display on the TV screen 1302.

The simulation module 208 is permanently connected to a TV screen 1302which displays in the two modes the field of interest, all detectedmoving patterns labeled with their specific classification andrecognition along with some potential alarm setting.

The simulation module 208 is connected to a data storage whichcontributes to generate a big data record system including the following

-   -   1. All simulations performed algorithmically or humanly for        training and updating the system.    -   2. All information received and decoded in real time from the        telecommunication network as resulting from the current        surveillance activities.

This big data record will be analyzed as background work on given timespans such as daily, weekly, monthly, yearly to discover new unforeseenpattern situations that may be missing in the initial or updatingtrainings and help to induce new updates of the system.

The Deep Q-Learning Module 210

The Deep Q-learning module 210 works like the unconscious part of thehuman brain which, after learning and updating from experiments gainedfrom the environment, analyzes and makes fast recognitions anddecisions. This part has the essence of a bottom-up approach, that oneof empiricism.

The Deep Q-learning module 210 is trained from both the real field andthe calibrated simulation module 208 before the start of operations, andafterwards, at the occurrence of both modifications of the field orunpredicted events. The Deep Q-learning module 210 receives the fieldinformation from the simulation module 208 which decodes and locates theinformation received from the telecommunication network in real time onthe three-dimensional topographic representation of the field. The DeepQ-learning module 210 receives information from all connected passiveand active motion sensors to perform motion classification, trajectorybuilding, prediction of abnormalities, incidents or accidents. The DeepQ-learning module 210 receives limited stream or motion-related segmentsof information from video cameras to perform pattern recognition usingan established and real time updated data base. All data after analysisare transmitted to the simulation module 208 to label all movingpatterns on the screen with the recognized characteristics, signaleither unclassified or unrecognized patterns or the potentiality ofabnormalities, incidents or accidents.

The Deep Q-learning module 210 is supervised and controlled by theExpert system module 302 through an adaptive dual control principle.

The Expert System Module 302

The expert system module 302 is divided into two parts as follows.

1. A controlling expert system module 302.

2. A big data analytics expert system module 302.

The Controlling Expert system module 302 works like the conscious partof the human brain and makes accurate analysis but at a slower pace thanthe deep Q-learning. It has the essence of a top-down approach, that oneof rationalism. The Controlling Expert system module 302 implements theaccurate/true models of mechanics (motion) and physics (sensors) takinginto account the field topography. The controlling expert system module302 analyzes the motion information with a redundant basis of analyzingfunctions that constitute of a dictionary to decompose the sensedsignals into its motion components. This part refers to the digitalsignal analysis theory here extended to process signals generated fromscattered sensor grids capturing wave transformations that occurred inthe field due to motion and in the sensor field of view due to theelectronics/photonics effects. The Controlling Expert system module 302can build and then work on an established and updatable data base ofanalyzing functions roughly working as match filters. The analyzingfunctions are constructions based on Lie group representations of motionand waves as digitized continuous wavelets (Generalization of theFourier Transform). The kinematic parameter estimation is performed asfilter matching though an inverse problem technique. The analyzingfunction needs to be calibrated along with the simulation module 208before the start of the system. Motion trajectory construction is basedon resolving an Euler-Lagrange Equation which comes to an algorithm. Inthis algorithm, each trajectory is the locus that optimizes a Lagrangianfunction through a dynamic programming algorithm that can be rewrittenin a recursive form known as Bellman's equation. The dynamic programmingalgorithm is deep learning implemented in the Q-Learning system allbecoming neuro-dynamic programming with Q-learning function as state ofa neural network with approximations leading to a gradient algorithm.For kinematic parameter estimation as well as trajectory building, thecontrolling system supervises and validates the outcome of the DeepQ-learning in an adaptive dual control. In predictable situations, theadaptive control regulates and the deep Q-learning outcome is prevailingto display the results in the simulation module 208. In situations thatbecome unpredictable, the expert system module 302 is taking over withthe simulation module 208 in order to update and improve the trainingthe deep Q-learning module 210 and alert the human supervisor of theactions to be taken.

The big-data analytics expert system module 302 works on the all thepast-accumulated data. Over days, weeks and months, all data produced bythe connected sensor network and decoded in the simulation module 208are recorded and archived which generates a big data system. Thebig-data analytics system performs predictive analytics which consist ofextracting information from the existing big data set in order todetermine and characterize specific moving behavior patterns and be ableto predict future situations, abnormalities, incidents and accidents andto explore unusual events or situations all with more and moreefficiency. The big-data analytics also will produce all forms ofcustomized statistics over day, week, month and year ranges.

The Locked Mode

The locked mode is an additional operative mode of the system where thehuman supervisor or the artificial intelligent system may focus andfreeze on specific moving patterns of interest with the following tools.

-   -   1. Add at least one TV screen 1302 which will display the video        streams coming from the cameras (one or more) which fields of        view cover the pattern of interest. The cameras involved in this        tracking will keep on changing automatically according to their        respective fields of view and the trajectory taken by the moving        pattern of interest in order to trace all the tour and be able        to react on the moving pattern at any time or any position of        its tour.    -   2. Add TV screen 1302 s for local moving cameras installed on        moving robots, drones or human security guards.

Freeze mode is a locked control property that comes as an additionalcapability to the adaptive dual control performed by the deep Q-learningmodule 210 and expert system module 302. All data generated by inducedfreeze mode are recorded for long term on the big data storage.

Further, in the inverse problem, detection and motion analysis may besolved by a dual control process functioning on a deep learning neuralnetwork and an expert system. The way a dual control implements anadaptive optimal control 1718 may be pictured in FIG. 17. On situationof interest, an algorithm 1700 may freeze 1706 on specific patterns.Depending on a predictability 1702 or an unpredictability 1704 of theenvironment, the algorithm 1700 may make decisions based on two or moreavailable chains of command such as regulate 1712, learning 1714,caution 1716.

Further, periods where the environment may be predictable, correspond tosituations that have been learned during the training. On predictablesituations, the deep learning algorithm (such as the algorithm 1700) maywork as a stand-alone process that takes actions that rely to itstraining, meaning the training originally received at the initiation ofthe system or the latest training update. During the training periods,the weights or the hyper-parameters of the neural network were computedand adjusted for optimal motion analysis.

Further, on situations where the environment deviates from an acquiredstatistics and become unpredictable, the deep learning algorithm (suchas the algorithm 1700) may take actions that refer to an exact model.The so-called expert system performs the optimal motion analysis but ata lower speed. The deep learning algorithm may need to be retrained orupdated to the new environment statistics.

Further, on special situations where the neural network may rely onadditional accurate motion measurements made by an active system (likeDoppler measurements through ultrasonic, microwave or laser systems), asupervisor may freeze 1706 the control on the measurements performed bythe active system. Applications of a locked control may also beimplemented as the capture by a robot of a pattern moving in the field.

Further, the Q-learning function of the deep learning algorithm mayallow the action to be selected from different sources. In thisapplication, an adaptive process may be implemented and the actions tobe taken can be determined following two control patterns which may be adual control 1710 and a locked control 1708.

The dual control 1710 differentiates between situations that may bepredictable to situations that are unpredictable. In a predictableenvironment where the model statistics are unchanged and correspond tothe last training update, the action to be taken may follow and rely onthe neural network supervised by the expert system. In situations wherethe model statistics may have or have changed, the environment becomesunpredictable. Exercising caution and learning become the prevailingrules. The determination of the optimal action to be taken may bechanged by the supervisor in three different ways. First, follow theaction computed by the expert system. Second, explore the newenvironment to learn. Third, follow the action computed from anothersource of measurements.

Further, the locked control 1708 may correspond to a possibility givento the supervisor to freeze 1706 on the system on a given target ofinterest. Further, latter option may be especially useful and efficientwhere active motion estimation may be performed through precisemeasurements using ultrasonic or laser systems and may be entered asselected action.

The equivalence of on adaptive dual control and an artificialintelligence based on an expert system and a Q-learning system ispresented in FIG. 18. As shown, the algorithm may employ artificialintelligence 1802, and model based expert system 1804. Further,Q-learning 1806 may lead to action 1808, which may affect environment1812, thereby providing a deep learning based experience.

Alternative techniques of motion sensor networks can be implemented withthe same A.I. as the one described in the application layer. In thosecases, it involves the introduction of one or multiple active sources ofwaves but would proceed with the same schemes and procedures oftelecommunicating and monitoring in the remote center. Two active motionsensor networks are considered here which are namely a network ofultrasonic motion sensors and a network of microwave motion sensors.Both types of sensors are also located at the physical layer of thesystem in the field like any other motion sensors. Those systems requirebi-directional transmissions of information: bottom-up withconcentration of sensed motion information towards the remote center andtop-down with remote center commands sent to adapt local emission modes.

A network of ultrasonic motion sensors is spread in the field or in someareas of the field. Ultrasonic sensors are attached on surfaces in thesame way as the photo-detection-based motion sensors. This networkset-up requires to install one or more (a variety of) ultrasoundssources in key locations of the field. The frequency range normallyemployed in ultrasonic detection is from 100 KHz to 50 MHz. This activeband is to be too high for normal human ear which is not able to detectsounds. Normal human ear detection is located in the range 20 Hz to 20KHz. Ultrasonic motion sensor networks work with having individualsources emitting ultrasonic waves all in synchronism in form of impulsesor chirps with programmable frequency, length, interval delays orpatterns. Distributed motion sensors sense the reflected waves andcompare with their background reference, at least, in term of differenceof time, and if more sophisticated, in terms of difference of shape,duration, intensity and frequencies. All relevant motion-differential(or total) information are transmitted through the telecommunicationnetwork to the remote monitoring.

The implementation of an inverse problem technique is required toestimate/infer the values of kinematic parameters associated to eachmoving patterns in terms of position, speed, shape and orientation.Inverse problem technique needs to be implemented in each three parts ofthe A.I. which are namely the Simulator, the Deep Q-learning System andthe Expert System. Each part of the A.I. system is requesting training,calibration and simulations as described. The Deep Q-learning cannaturally incorporate the resolution of the inverse problem since bothworking through gradient algorithm-based estimations.

Ultrasonic motion sensor networks can be deploy as a substitute or inaddition to existing photo-electric sensors covering a part or thetotality of the field of interest. Ultrasonic motion sensor networks areespecially useful in applications where photoelectric sensors cannotwork of be deployed as a result of the medium like in water or in smokyenvironments. The velocity of ultrasounds at a particular time andtemperature is constant in a medium.

This system is similar to the way how bats generate from their throatschirps with specific ultrasonic frequencies, shapes, lengths andpatterns and measure through their ears the time et frequency shiftsinduced by the chirp hitting an object. In this application, the earsystem is now spread in the field of interest in form of a detectingsensor network.

A network of microwave motion sensors is spread in the field or in someareas of the field. Microwave sensors are attached on surfaces in thesame way as the photo-detection-based motion sensors. This networkset-up requires to install one or more (a variety of) microwave sourcesin key locations of the field. Microwave are electro-magnetic waveswhose frequency bands range from 0.3 GHz to 300 GHz. Microwave sensorsand sources work in whole similarity with their ultrasonic correspondingcomponents. Microwave motion sensor networks work with having individualsources emitting ultrasonic waves either continuously or withsynchronism in form of impulses of programmable frequency, length,interval delays or patterns. Distributed motion sensors in the area ofreception sense the reflected waves and compare with their backgroundreference, at least, in term of frequency shift (Doppler's effect forspeed/velocity estimation) and phase shift for delays, and if moresophisticated, in terms of difference of shape, duration, intensity andfrequencies. All relevant motion-differential (or total) information aretransmitted through the telecommunication network to the remotemonitoring.

The implementation of an inverse problem technique is required toestimate/infer the values of kinematic parameters associated to eachmoving patterns in terms of position, speed, shape and orientation.Inverse problem technique needs to be implemented in each three parts ofthe A.I. which are namely the Simulator, the Deep Q-learning System andthe Expert System. Each part of the A.I. system is requesting training,calibration and simulations as described. The Deep Q-learning cannaturally incorporate the resolution of the inverse problem since bothworking through gradient algorithm-based estimation. Microwave motionsensor networks can be deployed as a substitute or in addition toexisting photo-electric sensors covering a part or the totality of thefield of interest.

Unlike other waves, microwave sources may have narrow beam that impartsit with the characteristic features like broad bandwidth and high datatransmission. Microwave motion sensor network can be used in harshenvironment where heat cycles are not regular and can also penetratethrough walls, holes and can be employed to impart coverage across theboundary/closings. The networking approach with the A.I. system would beable to disambiguate false alarm occurrence better than any othersystems in place. Special applications are prisons, banks, warehouses,museums and more.

With reference to FIG. 20, a system consistent with an embodiment of thedisclosure may include a computing device or cloud service, such ascomputing device 2000. In a basic configuration, computing device 2000may include at least one processing unit 2002 and a system memory 2004.Depending on the configuration and type of computing device, systemmemory 2004 may comprise, but is not limited to, volatile (e.g.random-access memory (RAM)), non-volatile (e.g. read-only memory (ROM)),flash memory, or any combination. System memory 2004 may includeoperating system 2005, one or more programming modules 2006, and mayinclude a program data 2007. Operating system 2005, for example, may besuitable for controlling computing device 2000's operation. In oneembodiment, programming modules 2006 may include image-processingmodule, machine learning module. Furthermore, embodiments of thedisclosure may be practiced in conjunction with a graphics library,other operating systems, or any other application program and is notlimited to any particular application or system. This basicconfiguration is illustrated in FIG. 20 by those components within adashed line 2008.

Computing device 2000 may have additional features or functionality. Forexample, computing device 2000 may also include additional data storagedevices (removable and/or non-removable) such as, for example, magneticdisks, optical disks, or tape. Such additional storage is illustrated inFIG. 20 by a removable storage 2009 and a non-removable storage 2010.Computer storage media may include volatile and non-volatile, removableand non-removable media implemented in any method or technology forstorage of information, such as computer-readable instructions, datastructures, program modules, or other data. System memory 2004,removable storage 2009, and non-removable storage 2010 are all computerstorage media examples (i.e., memory storage.) Computer storage mediamay include, but is not limited to, RAM, ROM, electrically erasableread-only memory (EEPROM), flash memory or other memory technology,CD-ROM, digital versatile disks (DVD) or other optical storage, magneticcassettes, magnetic tape, magnetic disk storage or other magneticstorage devices, or any other medium which can be used to storeinformation and which can be accessed by computing device 2000. Any suchcomputer storage media may be part of device 2000. Computing device 2000may also have input device(s) 2012 such as a keyboard, a mouse, a pen, asound input device, a touch input device, a location sensor, a camera, abiometric sensor, etc. Output device(s) 2014 such as a display,speakers, a printer, etc. may also be included. The aforementioneddevices are examples and others may be used.

Computing device 2000 may also contain a communication connection 2016that may allow device 2000 to communicate with other computing devices2018, such as over a network in a distributed computing environment, forexample, an intranet or the Internet. Communication connection 2016 isone example of communication media. Communication media may typically beembodied by computer readable instructions, data structures, programmodules, or other data in a modulated data signal, such as a carrierwave or other transport mechanism, and includes any information deliverymedia. The term “modulated data signal” may describe a signal that hasone or more characteristics set or changed in such a manner as to encodeinformation in the signal. By way of example, and not limitation,communication media may include wired media such as a wired network ordirect-wired connection, and wireless media such as acoustic, radiofrequency (RF), infrared, and other wireless media. The term computerreadable media as used herein may include both storage media andcommunication media.

As stated above, a number of program modules and data files may bestored in system memory 2004, including operating system 2005. Whileexecuting on processing unit 2002, programming modules 2006 (e.g.,application 2020 such as a media player) may perform processesincluding, for example, one or more stages of methods, algorithms,systems, applications, servers, databases as described above. Theaforementioned process is an example, and processing unit 2002 mayperform other processes. Other programming modules that may be used inaccordance with embodiments of the present disclosure may includemachine learning applications.

Generally, consistent with embodiments of the disclosure, programmodules may include routines, programs, components, data structures, andother types of structures that may perform particular tasks or that mayimplement particular abstract data types. Moreover, embodiments of thedisclosure may be practiced with other computer system configurations,including hand-held devices, general purpose graphics processor-basedsystems, multiprocessor systems, microprocessor-based or programmableconsumer electronics, application specific integrated circuit-basedelectronics, minicomputers, mainframe computers, and the like.Embodiments of the disclosure may also be practiced in distributedcomputing environments where tasks are performed by remote processingdevices that are linked through a communications network. In adistributed computing environment, program modules may be located inboth local and remote memory storage devices.

Furthermore, embodiments of the disclosure may be practiced in anelectrical circuit comprising discrete electronic elements, packaged orintegrated electronic chips containing logic gates, a circuit utilizinga microprocessor, or on a single chip containing electronic elements ormicroprocessors. Embodiments of the disclosure may also be practicedusing other technologies capable of performing logical operations suchas, for example, AND, OR, and NOT, including but not limited tomechanical, optical, fluidic, and quantum technologies. In addition,embodiments of the disclosure may be practiced within a general-purposecomputer or in any other circuits or systems.

Embodiments of the disclosure, for example, may be implemented as acomputer process (method), a computing system, or as an article ofmanufacture, such as a computer program product or computer readablemedia. The computer program product may be a computer storage mediareadable by a computer system and encoding a computer program ofinstructions for executing a computer process. The computer programproduct may also be a propagated signal on a carrier readable by acomputing system and encoding a computer program of instructions forexecuting a computer process. Accordingly, the present disclosure may beembodied in hardware and/or in software (including firmware, residentsoftware, micro-code, etc.). In other words, embodiments of the presentdisclosure may take the form of a computer program product on acomputer-usable or computer-readable storage medium havingcomputer-usable or computer-readable program code embodied in the mediumfor use by or in connection with an instruction execution system. Acomputer-usable or computer-readable medium may be any medium that cancontain, store, communicate, propagate, or transport the program for useby or in connection with the instruction execution system, apparatus, ordevice.

The computer-usable or computer-readable medium may be, for example butnot limited to, an electronic, magnetic, optical, electromagnetic,infrared, or semiconductor system, apparatus, device, or propagationmedium. More specific computer-readable medium examples (anon-exhaustive list), the computer-readable medium may include thefollowing: an electrical connection having one or more wires, a portablecomputer diskette, a random-access memory (RAM), a read-only memory(ROM), an erasable programmable read-only memory (EPROM or Flashmemory), an optical fiber, and a portable compact disc read-only memory(CD-ROM). Note that the computer-usable or computer-readable mediumcould even be paper or another suitable medium upon which the program isprinted, as the program can be electronically captured, via, forinstance, optical scanning of the paper or other medium, then compiled,interpreted, or otherwise processed in a suitable manner, if necessary,and then stored in a computer memory.

Embodiments of the present disclosure, for example, are described abovewith reference to block diagrams and/or operational illustrations ofmethods, systems, and computer program products according to embodimentsof the disclosure. The functions/acts noted in the blocks may occur outof the order as shown in any flowchart. For example, two blocks shown insuccession may in fact be executed substantially concurrently or theblocks may sometimes be executed in the reverse order, depending uponthe functionality/acts involved.

While certain embodiments of the disclosure have been described, otherembodiments may exist. Furthermore, although embodiments of the presentdisclosure have been described as being associated with data stored inmemory and other storage mediums, data can also be stored on or readfrom other types of computer-readable media, such as secondary storagedevices, like hard disks, solid state storage (e.g., USB drive), or aCD-ROM, a carrier wave from the Internet, or other forms of RAM or ROM.Further, the disclosed methods' stages may be modified in any manner,including by reordering stages and/or inserting or deleting stages,without departing from the disclosure.

Although the present disclosure has been explained in relation to itspreferred embodiment, it is to be understood that many other possiblemodifications and variations can be made without departing from thespirit and scope of the disclosure.

I claim:
 1. A system for performing motion analysis in a field ofinterest, the system comprising: a plurality of motion sensorsconfigured to be disposed in the field of interest, wherein theplurality of motion sensors is configured to generate a plurality ofmotion data corresponding to at least one motion of at least one objectin the field of interest; a communication device configured forreceiving configuration data associated with the field of interest fromat least one data source; a processing device configured for: generatinga digital model corresponding to the field of interest based on theconfiguration data using a simulation module; generating at least one ofa plurality of motion signatures corresponding to a plurality ofpredetermined motions and a plurality of object signatures correspondingto a plurality of predetermined objects based on the digital model usingthe simulation module; performing training of a deep Q-learning modulebased on at least one of the plurality of motion signatures and theplurality of object signatures; performing a first analysis of theplurality of motion data based on the deep Q-learning module; andgenerating at least one trajectory data corresponding to at least onetrajectory associated with the at least one object based on the firstanalysis using the deep Q-learning module; and a storage deviceconfigured for storing the digital model and at least one of theplurality of motion signatures and the plurality of object signatures;performing a second analysis of the plurality of motion data based on anexpert system module, wherein the generating of the at least onetrajectory data is based further on the second analysis; whereinperforming the second analysis comprises: generating Galilei waveletsbased on a plurality of kinematic parameters, wherein the Galileiwavelets are group representations computed from extended Galileigroups, wherein the plurality of kinematic parameters is computed asspatio-temporal functions digitized in the space of the plurality ofmotion data, wherein the Galilei wavelets facilitate the analysis of thespatio-temporal functions transformed by motion; and estimating at leastone kinematic parameter based on the Galilei wavelets, wherein theestimating is performed using an inverse problem technique based on agradient algorithm with at least one objective function whosecomputation is based on the digitized Galilei wavelet transform, whereinthe estimating of at least one motion trajectory is further performed bydynamic programming using Bellman's recursive techniques, wherein a costfunction is optimized using at least one Lagrangian function whosecomputation is based on the digitized Galilei wavelet transform.
 2. Thesystem of claim 1, wherein the processing device is configured forperforming predictive analytics based on historical data associated withmotion analysis using the expert system module, wherein the generatingof the at least one trajectory data is further based on the predictiveanalytics.
 3. The system of claim 1, wherein the performing of thesecond analysis of the plurality of motion data is based on a physicsmodel and a field of interest model.
 4. The system of claim 1, whereinthe expert system module supervises and validates an output of the deepQ-learning module based on an adaptive dual control, wherein in anunpredictable scenario, the expert system module performs at least oneof training and updating of the deep Q-learning module based on thesecond analysis.
 5. The system of claim 1, wherein configuration datacomprises at least one of at least one motion sensor characteristic, atleast one object characteristic, at least one light sourcecharacteristic, at least one active source characteristic, at least onegateway characteristic and at least one field characteristic.
 6. Thesystem of claim 1, wherein the digital model comprises a motion sensormodel associated with a motion sensor of the plurality of motionsensors, an object model associated with an object of the at least oneobject, a light source model associated with a light source of theplurality of light sources, an active source model associated with anactive source of the plurality of active sources, a video camera modelassociated with a video camera of the plurality of video cameras, agateway model associated with a gateway of the at least one gateway, afield of interest model associated with the field of interest and aremote monitoring center model associated with a remote monitoringcenter.
 7. The system of claim 6, wherein the object model comprises aplurality of object models corresponding to a plurality of predeterminedobjects, wherein a plurality of object signatures corresponds to theplurality of predetermined objects, wherein the plurality of objectsignatures comprise a plurality of motion sensor data associated withthe plurality of motion sensors, wherein the plurality of object modelsis determined based on at least one of systematically varying the atleast one object characteristic and a strategic input received from aninput device operated by a human expert.
 8. The system of claim 6,wherein the motion of the object model comprises a plurality ofpredetermined motions, wherein a plurality of motion signaturescorresponds to the plurality of predetermined motions, wherein theplurality of motion signatures comprise a plurality of motion sensordata associated with the plurality of motion sensors.
 9. The system ofclaim 6 further comprising a change detection sensor configured todetect a change in the field of interest, wherein the processing deviceis further configured for triggering training of the deep Q-learningmodule based on at least one of the change and detection of anunpredictable event associated with the at least one trajectory data.10. The system of claim 6, wherein the motion sensor model comprises atleast one motion sensor characteristic of the motion sensor, wherein theat least one motion sensor characteristic comprises at least oneoperational characteristic, wherein the at least one operationalcharacteristic comprises a type of the motion sensor, a sensitivity ofthe motion sensor, a range of detection of the motion sensor, an angleof aperture of the motion sensor, a resolution of the motion sensor, anaccuracy of the motion sensor, a precision of the motion sensor, alinearity of the motion sensor and a time response of the motion sensor,wherein the at least one motion sensor characteristic comprises at leastone dispositional characteristic, wherein the at least one dispositionalcharacteristic comprises at least one of a position of the motion sensorand an orientation of the motion sensor.
 11. The system of claim 6,wherein the light source model comprises at least one light sourcecharacteristic of the light source, wherein the at least one lightsource characteristic comprises at least one of a type of light source,a position of the light source, an orientation of the light source, anintensity of the light source, a duty cycle of the light source, aspectral band of the light source, a thermal spectral band associatedwith infrared sources, a radiation pattern of the light source and arange of illumination of the light source.
 12. The system of claim 1further comprising: a plurality of video cameras disposable at aplurality of key locations in the field of interest, wherein each videocamera is configured to capture image sequences associated with aportion of the field of interest, wherein at least one video camera isfurther configured to transmit a part of a corresponding image sequenceto a remote monitoring center through at least one gateway; and at leastone gateway disposable proximal to the field of interest, wherein the atleast one gateway is configured as a two-way interface capable ofcommunicating with the remote monitoring center and the plurality ofmotion sensors, wherein the remote monitoring center comprises theprocessing device, wherein the analyzing is further based on the imagesequences.
 13. The system of claim 1, wherein the processing device isfurther configured for: analyzing the at least one trajectory data basedon at least one predetermined rule; and identifying at least one eventof interest based on the analyzing of the at least one trajectory data.14. The system of claim 1, wherein performing training of the deepQ-learning module comprises generating the at least one predeterminedrule.
 15. The system of claim 1, wherein the processing device isfurther configured for activating at least one tracker based onidentifying of the at least one event, wherein the at least one trackeris configured for controlling at least one operational state of theplurality of motion sensors in order to track the at least one objectassociated with the at least one event of interest.
 16. The system ofclaim 1, wherein the digital model comprises a three-dimensional visualrepresentation of the field of interest, wherein the system furthercomprises a display device configured for displaying thethree-dimensional visual representation.
 17. The system of claim 1,wherein the system further comprises a plurality of active sourcesconfigured to emit source waves, wherein the plurality of motion sensorsis configured to receive reflected waves corresponding to the sourcewaves, wherein the plurality of motion sensors comprises at least one ofa plurality of ultrasonic motion sensors and a plurality of microwavemotion sensors, wherein the processing device is configured for:determining at least one characteristic difference between at least onesource characteristic associated with the source waves and at least onereflected characteristic associated with the reflected waves; andestimating at least one kinematic parameter associated with the at leastone object in the field of interest based on the at least onecharacteristic difference.
 18. The system of claim 17, wherein thecommunication device is further configured for receiving a plurality ofcommands from at least one gateway communicatively coupled with thecommunication device, wherein the plurality of active sources isconfigured to operate in at least one of a plurality of emission modesbased on the plurality of commands, wherein an emission mode of theplurality of emission modes is characterized by at least one of afrequency of emission, a length of emission, a delay interval betweenconsecutive emissions and a pattern of emission.